Journal of Algebra and Its Applications
Journal Prestige (SJR): 0.69 Number of Followers: 3 Hybrid journal (It can contain Open Access articles) ISSN (Print) 02194988  ISSN (Online) 17936829 Published by World Scientific [120 journals] 
 A talented monoid view on Lie bracket algebras over Leavitt path algebras

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Authors: Wolfgang Bock, Alfilgen Sebandal, Jocelyn Vilela
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we study properties such as simplicity, solvability and nilpotency for Lie bracket algebras arising from Leavitt path algebras, based on the talented monoid of the underlying graph. We show that graded simplicity and simplicity of the Leavitt path algebra can be connected via the Lie bracket algebra. Moreover, we use the Gelfand–Kirillov dimension for the Leavitt path algebra for a classification of nilpotency and solvability.
Citation: Journal of Algebra and Its Applications
PubDate: 20220514T07:00:00Z
DOI: 10.1142/S0219498823501700

 Powers of edge ideals of weighted oriented graphs with linear resolutions

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Authors: Arindam Banerjee, Kanoy Kumar Das, S. Selvaraja
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a weighted oriented graph and [math] denote the corresponding edge ideal. In this paper, we give a combinatorial characterization of [math] which has a linear resolution. As a consequence, we prove that if [math] is the edge ideal of a weighted oriented graph [math], then [math] has a linear resolution if and only if all powers of [math] have a linear resolution. Also, we prove that if [math] is a weighted oriented graph and [math] for all [math], then [math] has a linear resolution if and only if all powers of [math] have linear quotients. We provide a lower bound for the regularity of powers of edge ideals of weighted oriented graphs in terms of induced matching. Finally, we obtain a general upper bound for the regularity of edge ideals of weighted oriented graphs.
Citation: Journal of Algebra and Its Applications
PubDate: 20220512T07:00:00Z
DOI: 10.1142/S0219498823501487

 Commutators in groups of order [math]

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Authors: Rahul Kaushik, Manoj K. Yadav
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we present a characterization of groups [math] of order [math], [math] prime, in which not all elements of the commutator subgroup [math] of [math] are commutators in [math]. In the way, we obtain several structural results on groups of order [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220512T07:00:00Z
DOI: 10.1142/S021949882350158X

 Reductions and cores of ideals in trivial ring extensions

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Authors: S. Kabbaj, A. Mimouni
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
This paper contributes to the study of reductions and cores of ideals in commutative rings. We pursue our investigation initiated in our previous research works on reductions and core, but this time, in settings with zerodivisors. Namely, we study reductions and cores of ideals in various contexts of trivial ring extensions. Section 2 presents preliminary results on reductions and core in generic trivial extensions and Sec. 3 investigates reductions and cores of arbitrary ideals (i.e. not necessarily saturated) in trivial extensions issued from special categories of modules. All results are illustrated with original examples in Sec. 4.
Citation: Journal of Algebra and Its Applications
PubDate: 20220512T07:00:00Z
DOI: 10.1142/S0219498823501591

 Sylowtype theorems for generalized digroups

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Authors: José Gregorio RodríguezNieto, Olga Patricia SalazarDíaz, Raúl Velásquez
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Generalized digroups are considered a nontrivial extension of the concept of group, thus one might think that many definitions and results on group theory can be naturally extended to generalized digroups. In this paper, we prove that it is not always true, since we do not have a version of Lagrange’s theorem for generalized digroups. On the other side, we propose and study Sylowtype theorems for generalized digroups.
Citation: Journal of Algebra and Its Applications
PubDate: 20220512T07:00:00Z
DOI: 10.1142/S0219498823501621

 On triple homomorphisms of Lie algebras

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Authors: Mohammad Hossein Jafari, Ali Reza Madadi, Gunnar Traustason
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] and [math] be two Lie algebras over a commutative ring with identity. In this paper, under some conditions on [math] and [math], it is proved that every triple homomorphism from [math] onto [math] is the sum of a homomorphism and an antihomomorphism from [math] into [math]. We also show that a finitedimensional Lie algebra [math] over an algebraically closed field of characteristic zero is nilpotent of class at most [math] if and only if the sum of every homomorphism and every antihomomorphism on [math] is a triple homomorphism.
Citation: Journal of Algebra and Its Applications
PubDate: 20220512T07:00:00Z
DOI: 10.1142/S0219498823501682

 A note on integervalued skew polynomials

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Authors: Angelot Behajaina
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Given an integral domain [math] with quotient field [math], the study of the ring of integervalued polynomials [math] has attracted a lot of attention over the past decades. Recently, Werner has extended this study to the situation of skew polynomials. To be more precise, if [math] is an automorphism of [math], one may consider the set [math], where [math] is the skew polynomial ring and [math] is a “suitable” evaluation of [math] at [math]. For example, he gave sufficient conditions for [math] to be a ring and study some of its properties. In this paper, we extend the study to the situation of the skew polynomial ring [math] with a suitable evaluation, where [math] is a [math]derivation. Moreover we prove, for example, that if [math] is of finite order and [math] is a Dedekind domain with finite residue fields such that [math] is a ring, then [math] is nonNoetherian.
Citation: Journal of Algebra and Its Applications
PubDate: 20220512T07:00:00Z
DOI: 10.1142/S0219498823501712

 On partial augmentations of elements in integral group rings

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Authors: Victor Bovdi, Attila Maróti
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Inner relations are derived between partial augmentations of certain elements (units or idempotents) in group rings.
Citation: Journal of Algebra and Its Applications
PubDate: 20220512T07:00:00Z
DOI: 10.1142/S0219498823501724

 Primitive normal values of rational functions over finite fields

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Authors: Avnish K. Sharma, Mamta Rani, Sharwan K. Tiwari
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we consider rational functions [math] with some minor restrictions over the finite field [math] where [math] for some prime [math] and positive integer [math]. We establish a sufficient condition for the existence of a pair [math] of primitive normal elements in [math] over [math] Moreover, for [math] and rational functions [math] with quadratic numerators and denominators, we explicitly find that there are at most [math] finite fields [math] in which such a pair [math] of primitive normal elements may not exist.
Citation: Journal of Algebra and Its Applications
PubDate: 20220506T07:00:00Z
DOI: 10.1142/S0219498823501529

 Indecomposablity of top local cohomology modules and connectedness of the
prime divisors graphs
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Authors: Mohammad Reza Doustimehr
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an ideal of a Noetherian local ring [math] with [math] and [math] be a positive integer. In this paper, it is shown that the top local cohomology module [math] (equivalently, its Matlis dual [math]) can be written as a direct sum of [math] indecomposable summands if and only if the endomorphism ring [math] can be written as a direct product of [math] local endomorphism rings if and only if the set of minimal primes [math] of [math] with [math] can be written as disjoint union of [math] nonempty subsets [math] such that for all distinct [math] and all [math] and all [math], we have [math]. This generalizes Theorem 3.6 of Hochster and Huneke [Contemp. Math. 159 (1994) 197–208].
Citation: Journal of Algebra and Its Applications
PubDate: 20220506T07:00:00Z
DOI: 10.1142/S021949882350161X

 A note on a class of permutation trinomials

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Authors: Rohit Gupta, Amritanshu Rai
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] denote the finite field with [math] elements. In this paper, we investigate the trinomial [math] over the finite field [math], where [math] with [math] being a positive integer. We prove that the trinomial [math] permutes [math] if and only if [math] and [math] is even. This work is a continuation of the previous work of Bai and Xia [A new class of permutation trinomials constructed from Niho exponents,Cryptogr. Commun. 10 (2018) 1023–1036].
Citation: Journal of Algebra and Its Applications
PubDate: 20220506T07:00:00Z
DOI: 10.1142/S0219498823501633

 Counting the ideals with given genus of a numerical semigroup

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Authors: M. A. MorenoFrías, J. C. Rosales
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
If S is a numerical semigroup, denote by g(S) the genus of S. A numerical semigroup T is an I(S)semigroup if T\{0} is an ideal of S. If [math], then we denote by i(S,k) the number of I(S)semigroups with genus g(S) + k. In this work, we conjecture that [math] if [math], and we show that there is a term from which this sequence becomes stationary. That is, there exists [math] such that i(S, k˙S)= i(S, k˙S + h) for all [math] Moreover, we prove that the conjecture is true for ordinary numerical semigroups, that is, numerical semigroups which the form [math] for some positive integer. Additionally, we calculate the term from which the sequence becomes stationary.
Citation: Journal of Algebra and Its Applications
PubDate: 20220430T07:00:00Z
DOI: 10.1142/S0219498823300027

 Minimal orbit sizes in nilpotent group actions

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Authors: Thomas Michael Keller, Heng Lv, Guohua Qian, Dongfang Yang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let G be a finite nilpotent group. We prove the following results. (1) If G is of class 2 and acts faithfully and irreducibly on an elementary abelian group V, then all nontrivial orbits of G on V have sizes larger than [math]. (2) If G’ is cyclic, then every subgroup of G intersecting trivially with the center of G has order less than [math]. We also show that a result like (2) cannot be obtained when the hypothesis that G’ is cyclic is replaced by the hypothesis that the center of G is cyclic.
Citation: Journal of Algebra and Its Applications
PubDate: 20220430T07:00:00Z
DOI: 10.1142/S0219498823501530

 On some properties of Anuclei and [math]Anuclei of a quasigroup

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Authors: Dimpy Chauhan, Indivar Gupta, Rashmi Verma
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we investigate the properties of Anuclei and [math]Anuclei of a quasigroup including connections between components of [math]Anuclei and local identity elements. To make the study easier, we give the explicit structure of [math]Anuclei of a loop, a unipotent left loop and a unipotent right loop in terms of translation maps. We also find the left, right and middle Anuclei of a quasigroup which is an isostrophic image of a loop in terms of translation maps.
Citation: Journal of Algebra and Its Applications
PubDate: 20220430T07:00:00Z
DOI: 10.1142/S0219498823501578

 Irreducible modules for the loop of derivations of rational quantum torus

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Authors: Santanu Tantubay
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a rational quantum torus associated with the matrix q. Let [math] be the Lie algebra of derivations of [math]. In this paper, we consider the Lie algebra [math], where B is a commutative associative unital algebra over [math] and classify its irreducible modules with finitedimensional weight spaces.
Citation: Journal of Algebra and Its Applications
PubDate: 20220430T07:00:00Z
DOI: 10.1142/S0219498823501608

 Defining identities for mono and binary Zinbiel algebras

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Authors: Nurlan Ismailov, Farukh Mashurov, Nurken Smadyarov
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
An algebra is said to be a mono Zinbiel algebra if each of its onegenerated subalgebra is a Zinbiel algebra. An algebra is said to be a binary Zinbiel algebra if each of its twogenerated subalgebra is a Zinbiel algebra. We give an independent set of defining identities for mono and binary Zinbiel algebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20220430T07:00:00Z
DOI: 10.1142/S0219498823501657

 Zinbiel algebras are Nilpotent

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Authors: David A. Towers
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we show that every finitedimensional Zinbiel algebra over an arbitrary field is nilpotent, extending a previous result that they are solvable by other authors.
Citation: Journal of Algebra and Its Applications
PubDate: 20220430T07:00:00Z
DOI: 10.1142/S0219498823501669

 [math]Functions of Carlitz modules, resultantal varieties and rooted
binary trees, II
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Authors: A. Grishkov, D. Logachev, A. Zobnin
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We continue study of some algebraic varieties (called resultantal varieties) started in a paper of authors “Lfunctions of Carlitz modules, resultantal varieties and rooted binary trees, I”, cited as [4]. These varieties are related with the Sylvester matrix for the resultant of two polynomials, from one side, and with the Lfunctions of twisted Carlitz modules, from another side. They are described in terms of weighted rooted binary trees. We give some proofs that lack in [4], some examples and tables that confirm conjectures from [4], and some ideas of development of this theory.
Citation: Journal of Algebra and Its Applications
PubDate: 20220429T07:00:00Z
DOI: 10.1142/S0219498823501256

 Puresemisimplicity of the category of graded modules over graded artin
algebras
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Authors: Elham Mahdavi, Razieh vahed
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a [math]graded artin algebra. It is proved that the category of graded [math]modules is puresemisimple if and only if there are only finitely many nonisomorphic indecomposable finitely generated graded [math]modules. As a consequence of this result together with a known result of Gordon and Green (which states that [math] is of finite representation type if and only if there are only finitely many nonisomorphic indecomposable finitely generated graded [math]modules), we see that the category of all [math]modules is puresemisimple if and only if the category of all graded [math]modules is so.
Citation: Journal of Algebra and Its Applications
PubDate: 20220429T07:00:00Z
DOI: 10.1142/S0219498823501499

 Power series over integral domains of Krull type

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Authors: Le Thi Ngoc Giau, Phan Thanh Toan
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
An integral domain [math] is said to be of Krull type if [math] is a locally finite intersection of essential valuation overrings [math] of [math]. If each [math] is required to be onedimensional and discrete, then [math] is called a Krull domain. In this paper, we show that if [math] is an integral domain of Krull type such that some [math] is not an SFT ring, then the power series ring [math] is not a locally finite intersection of valuation domains. This is a generalization of our previous work, where [math] is assumed to be a valuation domain. It follows that [math] is a Krull domain if and only if both [math] and [math] are integral domains of Krull type, which is an improvement of a result by Paran and Temkin. We also prove that if [math] is a Prüfer domain, then [math] is a Krull domain if and only if [math] is an integral domain of Krull type.
Citation: Journal of Algebra and Its Applications
PubDate: 20220429T07:00:00Z
DOI: 10.1142/S0219498823501554

 Mutually unbiased special entangled bases with Schmidt number [math] in
[math]
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Authors: Qianqian Yan, Dengming Xu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we construct mutually unbiased special entangled bases with Schmidt number [math] in [math]. Precisely, we first provide a necessary and sufficient condition for two special entangled bases with Schmidt number [math] are mutually unbiased, and then use the condition to construct two mutually unbiased special entangled bases with Schmidt number 2 in [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220429T07:00:00Z
DOI: 10.1142/S0219498823501645

 Involutions of sl(2,k) and nonsplit, threedimensional simple Lie
algebras
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Authors: Philippe Meyer
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We give a process to construct nonsplit, threedimensional simple Lie algebras from involutions of [math], where [math] is a field of characteristic not two. Up to equivalence, nonsplit threedimensional simple Lie algebras obtained in this way are parametrized by a subgroup of the Brauer group of [math] and are characterized by the fact that their Killing form represents [math]. Over local and global fields we reexpress this condition in terms of Hilbert and Legendre Symbols and give examples of threedimensional simple Lie algebras which can and cannot be obtained by this construction over the field of rationals.
Citation: Journal of Algebra and Its Applications
PubDate: 20220420T07:00:00Z
DOI: 10.1142/S0219498823501396

 Character groups of dihedral and generalized quaternion groups

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Authors: Justin A. Stevenson, Jonathan D. H. Smith
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Finite abelian group duality appears in the discrete Fourier transform, or as the finite fragment of Pontryagin duality. The dual or character group of an abelian group encodes the products of its (linear) irreducible characters. Now, recent developments in combinatorics enable the construction of character groups for finite dihedral and generalized quaternion groups, encoding the products of all the irreducible characters (linear and nonlinear) in purely multiplicative fashion. In particular, just as in the abelian case, each dihedral group may serve as its own character group. Furthermore, certain Adams operations on the characters are shown to correspond to powers in the character group of a dihedral group.
Citation: Journal of Algebra and Its Applications
PubDate: 20220420T07:00:00Z
DOI: 10.1142/S0219498823501414

 Automorphisms of simple quotients of the Poisson and universal enveloping
algebras of [math]
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Authors: Altyngul Naurazbekova, Ualbai Umirbaev
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be the Poisson enveloping algebra of the Lie algebra [math] over an algebraically closed field [math] of characteristic zero. The quotient algebras [math] [math], where [math] is the standard Casimir element of [math] in [math] and [math], are proven to be simple in [U. Umirbaev and V. Zhelyabin, A Dixmier theorem for Poisson enveloping algebras, J. Algebra 568 (2021) 576–600]. Using a result by Makar–Limanov [22], we describe generators of the automorphism group of [math] and represent this group as an amalgamated product of its subgroups. Moreover, using similar results by Dixmier [Quotients simples de l’algebre enveloppante de [math], J. Algebra 24 (1973) 551–564] and O. Fleury [Sur les sousgroupes finis de [math] et [math], J. Algebra 200 (1998) 404–427] for the quotient algebras [math], where [math] is the standard Casimir element of [math] in the universal enveloping algebra [math], we prove that the automorphism groups of [math] and [math] are isomorphic.
Citation: Journal of Algebra and Its Applications
PubDate: 20220420T07:00:00Z
DOI: 10.1142/S0219498823501517

 Coserreness with respect to specialization closed subsets and some serre
subcategories
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Authors: Majid Rahro Zargar
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a specialization closed subset of [math] and [math] be a Serre subcategory of Mod R. As a generalization of the notion of cofiniteness, we introduce the concept of [math]coserreness with respect to [math] (see Definition 4.1). First, as a main result, for some special Serre subcategories [math], we show that an [math]module [math] with [math] is [math]coserre with respect to [math] if and only if [math] for all ideals [math]. Indeed, this result provides a partial answer to a question that was recently raised in [K. Bahmanpour, R. Naghipour and M. Sedghi, Modules cofinite and weakly cofinite with respect to an ideal, J. Algebra Appl. 16 (2018) 1–17]. As an application of this result, we show that the category of [math]coserre [math]modules [math] with [math] is a full Abelian subcategory of Mod R. Also, for every homologically bounded [math]complex [math] whose homology modules belong to [math] we show that the local cohomology modules [math] for all [math], are [math]coserre in all the cases where [math], [math] and [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823300015

 Skew left braces and isomorphism problems for Hopf–Galois structures
on Galois extensions
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Authors: Alan Koch, Paul J. Truman
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Given a finite group [math], we study certain regular subgroups of the group of permutations of [math], which occur in the classification theories of two types of algebraic objects: skew left braces with multiplicative group isomorphic to [math] and Hopf–Galois structures admitted by a Galois extension of fields with Galois group isomorphic to [math]. We study the questions of when two such subgroups yield isomorphic skew left braces or Hopf–Galois structures involving isomorphic Hopf algebras. In particular, we show that in some cases the isomorphism class of the Hopf algebra giving a Hopf–Galois structure is determined by the corresponding skew left brace. We investigate these questions in the context of a variety of existing constructions in the literature. As an application of our results we classify the isomorphically distinct Hopf algebras that give Hopf–Galois structures on a Galois extension of degree [math] for [math] prime numbers.
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823501189

 Generic GelfandTsetlin representations of [math] and [math]

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Authors: Jordan Disch
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We construct generic GelfandTsetlin representations of the [math]quantum groups [math] and [math]. These representations are infinitedimensional analogs to the finitedimensional irreducible representations provided by Gavrilik and Klimyk in [[math]deformed orthogonal and pseudoorthogonal algebras and their representations, Lett. Math. Phys. 21 (1991) 215–220]. They are quantum analogs of generic GelfandTsetlin representations constructed by Mazorchuk in [On GelfandZetlin modules over orthogonal Lie algebras, Algebra Colloq. 8 (2001) 345–360]. We give sufficient conditions for irreducibility and provide an upper bound for the length with the help of Casimir elements found by Molev, Ragoucy and Sorba.
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823501281

 Modules with chain condition on uncountably generated submoduled

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Authors: Maryam Davoudian
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we study modules with chain condition on uncountably generated submodules. We show that if an [math]module [math] satisfies the ascending chain condition on uncountably generated submodules, then its Goldie dimension is less than or equal to [math], where [math] is the first uncountable cardinal number. We also show that if a quotient finite dimensional module [math] satisfies the ascending chain condition on uncountably generated submodules, then it has Noetherian dimension and its Noetherian dimension is less than or equal to [math], where [math] is the first uncountable ordinal number. We also investigate that if a quotient finite dimensional module [math] satisfies the descending chain condition on uncountably generated submodules, then [math] has Krull dimension and its Krull dimension may be any ordinal number [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823501347

 Betti numbers of monomial ideals in four variables

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Authors: Guillermo Alesandroni
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We express the multigraded Betti numbers of monomial ideals in four variables in terms of the multigraded Betti numbers of 66 squarefree monomial ideals, also in four variables. We use this class of 66 ideals to prove that monomial resolutions in four variables are independent of the base field. In addition, we give a formula for the Betti numbers of an arbitrary monomial ideal in four variables.
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823501372

 Partial actions of a Hopf algebra on its base field and the corresponding
partial smash product algebra
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Authors: Grasiela Martini, Antonio Paques, Leonardo Duarte Silva
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduce the concept of a [math]Hopf algebra as a Hopf algebra obtained as the partial smash product algebra of a Hopf algebra and its base field, and show that every Hopf algebra is a [math]Hopf algebra. Moreover, a method to compute partial actions of a given Hopf algebra on its base field is developed and, as an application, we exhibit all partial actions of such type for some families of Hopf algebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823501402

 A note on the number of centralizers in finite ACgroups

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Authors: Julio C. M. Pezzott, Irene N. Nakaoka
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a finite ACgroup such that [math], where [math], [math] and [math] is odd. We prove that if [math] has [math] centralizers of elements, then [math], [math] is an even integer, the set of the sizes of the conjugacy classes of [math] is [math] and [math] is a Frobenius group whose Frobenius kernel is an elementary abelian [math]group of order [math] and the Frobenius complement is a group of order [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823501426

 On certain semigroups of transformations with restricted range

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Authors: De Biao Li, Wen Ting Zhang, Yan Feng Luo
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a finite chain and let [math] be the semigroup of all injective orderpreserving partial transformations on [math]. For any nonempty subset [math] of [math], let [math] be the subsemigroup of [math] of all transformations with range contained in [math]. In this paper, we characterize Green’s relations on [math], and show that the semigroup [math] is left abundant but not right abundant when [math] is a proper subset of [math]. Moreover, the cardinality and the rank of the semigroup [math] is determined.
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823501438

 A short note on polynomials [math], [math] even

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Authors: Daniele Bartoli, Matteo Bonini
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
An alternative proof of the necessary conditions on [math] for [math] to be a permutation polynomial in [math], [math] even, is given. This proof involves standard arguments from algebraic geometry over finite fields and fast symbolic computations.
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S021949882350144X

 Free symmetric pairs in the field of fractions of enveloping Lie algebras
with involution
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Authors: Jairo Z. Gonçalves
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a division ring with center [math], [math], let [math] be an involution of [math], and let [math] be the multiplicative group of [math]. A pair [math] is called free symmetric, if it is formed by symmetric elements, and it generates a free noncyclic subgroup of [math]. If [math] is the enveloping algebra of the nonabelian nilpotent Lie [math]algebra [math] over the field [math] of characteristic [math], and [math] is a [math]involution of [math] extended to the field of fractions [math] of [math], we show that [math] contains free symmetric pairs. We also discuss the consequences of symmetric elements of a normal subgroup being torsion over the center.
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823501451

 Local and 2local derivations on octonion algebras

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Authors: Shavkat Ayupov, Karimbergen Kudaybergenov, Allayar Allambergenov
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
This paper is devoted to study of local and 2local derivations on octonion algebras. We shall give a general form of local derivations on the real octonion algebra [math] This description implies that the space of all local derivations on [math] when equipped with Lie bracket is isomorphic to the Lie algebra [math] of all real skewsymmetric [math]matrices. We also consider [math]local derivations on an octonion algebra [math] over an algebraically closed field [math] of characteristic zero and prove that every [math]local derivation on [math] is a derivation. Further, we apply these results to similar problems for the simple sevendimensional Malcev algebra. As a corollary, we obtain that the real octonion algebra [math] and Malcev algebra [math] are simple nonassociative algebras which admit pure local derivations, that is, local derivations which are not derivation.
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823501475

 The automorphism group and fixing number of the orthogonality graph of the
full matrix ring
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Authors: Zhengxin Chen, Yu Wang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math], [math] be the set of all [math] matrices over a finite field [math], and [math] the subset of [math] consisting of all rank one matrices. In this paper, we first determine the automorphism group and the fixing number of the orthogonality graph of [math], and then characterize the automorphism group and the fixing number of the orthogonality graph of [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823501505

 A class of irreducible modules for loopVirasoro algebras

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Authors: Priyanshu Chakraborty, Punita Batra
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Tensor product of highest weight modules and intermediate modules for Virasoro algebra have been studied around 1997. Since then the irreducibility problem for tensor product of modules is open. We consider the loopVirasoro algebra [math], where Vir is the Virasoro algebra and [math] is a commutative associative unital algebra over [math]. In this paper, we study the irreducibility problem for the tensor product of highest weight modules and intermediate modules for [math]. Finally we found out a necessary and sufficient condition for such modules to be isomorphic.
Citation: Journal of Algebra and Its Applications
PubDate: 20220415T07:00:00Z
DOI: 10.1142/S0219498823501566

 Strong Gelfand pairs of SL([math])

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Authors: Andrea Barton, Stephen P. Humphries
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
A strong Gelfand pair [math] is a group [math] together with a subgroup [math] such that every irreducible character of [math] induces a multiplicityfree character of [math]. We classify the strong Gelfand pairs of the special linear groups [math], where [math] is a prime.
Citation: Journal of Algebra and Its Applications
PubDate: 20220412T07:00:00Z
DOI: 10.1142/S0219498823501335

 Classification of noncommutative conics associated to symmetric regular
superpotentials
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Authors: Haigang Hu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a [math]dimensional quantum polynomial algebra, and [math] a central regular element. The quotient algebra [math] is called a noncommutative conic. For a noncommutative conic [math], there is a finitedimensional algebra [math] which determines the singularity of [math]. In this paper, we mainly focus on a noncommutative conic such that its quadratic dual is commutative, which is equivalent to say, [math] is determined by a symmetric regular superpotential. We classify these noncommutative conics up to isomorphism of the pairs [math], and calculate the algebras [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220412T07:00:00Z
DOI: 10.1142/S0219498823501360

 On simpleinjective modules

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Authors: Yusuf Alagöz, Si̇nem Benli̇Göral, Engi̇n Büyükaşık
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
For a right module [math], we prove that [math] is simpleinjective if and only if [math] is min[math]injective for every cyclic right module [math]. The rings whose simpleinjective right modules are injective are exactly the right Artinian rings. A right Noetherian ring is right Artinian if and only if every cyclic simpleinjective right module is injective. The ring is [math] if and only if simpleinjective right modules are projective. For a commutative Noetherian ring [math], we prove that every finitely generated simpleinjective [math]module is projective if and only if [math], where [math] is [math] and [math] is hereditary. An abelian group is simpleinjective if and only if its torsion part is injective. We show that the notions of simpleinjective, strongly simpleinjective, socinjective and strongly socinjective coincide over the ring of integers.
Citation: Journal of Algebra and Its Applications
PubDate: 20220412T07:00:00Z
DOI: 10.1142/S0219498823501384

 A note on twogenerated ideals over domains

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Authors: Kui Hu, Jung Wook Lim, De Chuan Zhou
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a onedimensional Noetherian domain and [math] be a twogenerated fractional ideal of [math]. In this paper, we prove that [math] is [math]projective if and only if [math] and [math] are equivalent, i.e. there exists a projective fractional ideal [math] of [math] such that [math]. We also give an example to show that [math] being [math]projective does not necessarily imply that [math] and [math] are isomorphic.
Citation: Journal of Algebra and Its Applications
PubDate: 20220408T07:00:00Z
DOI: 10.1142/S0219498822502462

 Gorenstein and Cohen–Macaulay matching complexes

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Authors: Ashkan Nikseresht
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a simple undirected graph. The family of all matchings of [math] forms a simplicial complex called the matching complex of [math]. Here , we give a classification of all graphs with a Gorenstein matching complex. Also we study when the matching complex of [math] is Cohen–Macaulay and, in certain classes of graphs, we fully characterize those graphs which have a Cohen–Macaulay matching complex. In particular, we characterize when the matching complex of a graph with girth at least five or a complete graph is Cohen–Macaulay.
Citation: Journal of Algebra and Its Applications
PubDate: 20220405T07:00:00Z
DOI: 10.1142/S0219498823501463

 On finitely generated [math]flat modules over domains

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Authors: Kui Hu, Jung Wook Lim, De Chuan Zhou
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a domain. It is proved that if [math], then the class of finitely generated [math]flat modules and the class of finitely generated [math]projective modules coincide. It is also proved that an integrally closed domain [math] is a Prüfer domain if and only if [math], if and only if [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220331T07:00:00Z
DOI: 10.1142/S0219498822502450

 Some Cohen–Macaulay graphs arising from finite commutative rings

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Authors: T. Ashitha, T. Asir, M. R. Pournaki
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
For a given finite commutative ring [math] with [math], one may associate a graph which is called the total graph of [math]. This graph has [math] as the vertex set and its two distinct vertices [math] and [math] are adjacent exactly whenever [math] is a zerodivisor of [math]. In this paper, we give necessary and sufficient conditions for two classes of total graphs to be Cohen–Macaulay.
Citation: Journal of Algebra and Its Applications
PubDate: 20220331T07:00:00Z
DOI: 10.1142/S0219498823501293

 On the level property of twodimensional monomial ideals

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Authors: Phan Thi Thuy
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an ideal of the form I =⋂1≤i
Citation: Journal of Algebra and Its Applications
PubDate: 20220331T07:00:00Z
DOI: 10.1142/S0219498823501311

 Unitregularity of elements in rings

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Authors: TsiuKwen Lee
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
An element [math] in a unital ring [math] is said to have an inverse complement [math] if [math] is a unit of [math] and [math]. Unitregular elements are studied from the viewpoint of the existence of inverse complements. As a source of unitregular elements, we prove that if [math] is a completely reducible submodule of [math], then every element of [math] is unitregular if and only if any nonzero submodule of [math] is not square zero. This generalizes some results due to Stopar in 2020. Finally, extending the case of real or complex matrices to the context of rings, we characterize the outer and reflexive inverses of a given unitregular element depending only on its inverse complement.
Citation: Journal of Algebra and Its Applications
PubDate: 20220330T07:00:00Z
DOI: 10.1142/S0219498823501359

 An Engel condition with two generalized derivations on Lie ideals of prime
rings
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Authors: ChengKai Liu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a prime ring, let [math] be a noncentral Lie ideal of [math] and let [math] be two generalized derivations of [math]. In this paper, we characterize the structure of [math] and all possible forms of [math] and [math] such that [math] for all [math], where [math] are fixed positive integers. With this, several known results can be either deduced or generalized. In particular, we give a Lie ideal version of the theorem obtained by Lee and Zhou in [An identity with generalized derivations, J. Algebra Appl. 8 (2009) 307–317] and describe a more complete version of the theorem recently obtained by Dhara and De Filippis in [Engel conditions of generalized derivations on left ideals and Lie ideals in prime rings, Comm. Algebra 48 (2020) 154–167].
Citation: Journal of Algebra and Its Applications
PubDate: 20220328T07:00:00Z
DOI: 10.1142/S0219498823501153

 Amalgamated duplication of Banach algebras from homological point of view

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Authors: M. Abolghasemi, H. Javanshiri, Y. Tolooei
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In a paper from 2002, Zhang [Weak amenability of module extensions of Banach algebras, Trans. Amer. Math. Soc. 354 (2002) 4131–4151] used module extensions to construct an example of a weakly amenable Banach algebra which is not 3weakly amenable. Following his approach, we show that for amalgamated duplication of dual Banach algebras, we are able to choose appropriate conditions for weak Connes amenability of those Banach algebras which extend the Zhang’s result in a much more general setting. Moreover, apart from the characterization of minimal idempotents, we restrict our investigation to the study of injectivity, projectivity and flatness of amalgamated duplication of Banach algebras. Particularly, it is worth mentioning that our result paves the way for studying of homological properties and weak Connes amenability of those dual Banach algebras that have a semidirect productlike structure including Lau algebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20220328T07:00:00Z
DOI: 10.1142/S0219498823501165

 Quasiderivations of Lie–Yamaguti algebras

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Authors: Jie Lin, Liangyun Chen
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The concepts of derivation and centroid for Lie–Yamaguti algebras are generalized in this paper. A quasiderivation of a LYalgebra can be embedded as a derivation in a larger LYalgebra. The relationship between quasiderivations and robustness of Lie–Yamaguti algebras has been studied.
Citation: Journal of Algebra and Its Applications
PubDate: 20220328T07:00:00Z
DOI: 10.1142/S0219498823501190

 Finite symmetries of surfaces of [math]groups of coclass 1

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Authors: Siddhartha Sarkar
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The genus spectrum of a finite group [math] is a set of integers [math] such that [math] acts on a closed orientable compact surface [math] of genus [math] preserving the orientation. In this paper, we complete the full classification of spectrum sets of finite [math]groups of coclass [math], where [math] is an odd prime. As a consequence, it follows that for any prime [math] and a finite [math]group of coclass [math] of order [math] and exponent [math], there are at the most seven genus spectra despite the infinite growth of their isomorphism types along with [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220328T07:00:00Z
DOI: 10.1142/S0219498823501220

 Certain towers of ramified minimal ring extensions of commutative rings,
II
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Authors: David E. Dobbs
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an odd prime number and [math]. Assume that either [math]i[math] [math] or [math]ii[math] [math] and [math] is congruent to either [math] or [math] modulo [math] [math]respectively, assume that [math] and [math] is congruent to either [math] or [math] modulo [math]. Then there exist exactly five [math]respectively, exactly seven[math] isomorphism classes of rings [math] for which there exists a tower [math] of ramified [math]integral minimal[math] ring extensions such that [math] is the only ring properly contained between [math] and [math]. We produce a set of isomorphism class representatives of such [math] and, for each such [math], we show that, up to isomorphism, the corresponding ring [math] is the idealization [math]. One consequence, for each integer [math] whose primepower factorization [math] (with pairwise distinct prime numbers [math] and positive integers [math]) satisfies [math] for all [math], is a classification, up to isomorphism, of the rings that have cardinality [math] and exactly two proper (unital) subrings.
Citation: Journal of Algebra and Its Applications
PubDate: 20220328T07:00:00Z
DOI: 10.1142/S0219498823501244

 The classification of sharp permutation groups of type [math]

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Authors: S. Roghayeh Adhami, Douglas P. Brozovic
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The purpose of this paper is a classification of the nongeometric sharp permutation groups of type [math]. This, together with the work of Maund on geometric groups, yields a complete classification of sharp permutation groups of type [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220328T07:00:00Z
DOI: 10.1142/S0219498823501323

 On integral representations of finite groups and rings generated by
character values
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Authors: Dmitry Malinin
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We study realization fields and integrality of characters of finite subgroups of [math] and related lattices with a focus on the integrality of characters of finite groups [math]. We are interested in the arithmetic aspects of the integral realizability of representations of finite groups, order generated by the character values, the number of minimal realization splitting fields, and in particular, consider the conditions of realizability in the terms of Hilbert symbols and quaternion algebras and some orders generated by character values over the rings of rational and algebraic integers.
Citation: Journal of Algebra and Its Applications
PubDate: 20220324T07:00:00Z
DOI: 10.1142/S0219498823501207

 Prime ideal sum graph of a commutative ring

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Authors: Manideepa Saha, Angsuman Das, Ece Yetki̇n Çeli̇kel, Ci̇hat Abdi̇oğlu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative ring with identity. The prime ideal sum graph of [math], denoted by [math], is a graph whose vertices are nonzero proper ideals of [math] and two distinct vertices [math] and [math] are adjacent if and only if [math] is a prime ideal of [math]. In this paper, we study some connections between the graphtheoretic properties of this graph and some algebraic properties of rings. The clique number, the chromatic number and the domination number of the prime ideal sum graph for some classes of rings are studied. It is observed that under which condition [math] is complete. Moreover, the diameter and the girth of [math] are studied.
Citation: Journal of Algebra and Its Applications
PubDate: 20220324T07:00:00Z
DOI: 10.1142/S0219498823501219

 On global defensive [math]alliances in zerodivisor graphs of finite
commutative rings
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Authors: Driss Bennis, Brahim El Alaoui, Khalid Ouarghi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The global defensive [math]alliance is a very wellstudied notion in graph theory, it provides a method of classification of graphs based on relations between members of a particular set of vertices. In this paper, we explore this notion in zerodivisor graph of commutative rings. The established results generalize and improve recent work by Muthana and Mamouni who treated a particular case for [math] known by the global defensive alliance. Various examples are also provided which illustrate and delimit the scope of the established results.
Citation: Journal of Algebra and Its Applications
PubDate: 20220324T07:00:00Z
DOI: 10.1142/S021949882350127X

 Genus two nilpotent graphs of finite commutative rings

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Authors: G. Kalaimurugan, P. Vignesh, T. Tamizh Chelvam
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a finite commutative ring and [math] is nilpotent for some [math]. The nilpotent graph [math] of [math] is the simple undirected graph with vertex set [math] in which two vertices [math] and [math] are adjacent if and only if [math] is nilpotent. In this paper, we observe a relationship between zerodivisor graphs, essential graphs and nilpotent graphs of [math]. In continuation of genus characterizations in [T. Asir K. Mano and T. Tamizh Chelvam, Correction to: Classification of nonlocal rings with genus two zerodivisor graphs, Soft Comput. 25 (2021) 3355–3356; K. Selvakumar and M. Subajini, Finite commutative ring with genus two essential 10 graph, J. Algebra Appl. 16(2) (2018) 1850121], we classify all finite commutative rings (up to isomorphism) whose nilpotent graphs are of genus two.
Citation: Journal of Algebra and Its Applications
PubDate: 20220321T07:00:00Z
DOI: 10.1142/S0219498823501232

 Sums of commuting potent and nilpotent elements in rings

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Authors: Alexander Diesl
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
There has been a great deal of interest lately in studying rings in which every element can be written as a sum of potent elements and nilpotent elements. In this paper, we focus primarily on rings in which every element can be written as the sum of some number of [math]potent elements and a nilpotent (for some choice of [math]), all of which commute with each other. The research that has been conducted thus far in this area has revealed a number of interesting results and intriguing patterns. Our goal in this paper is to unify and extend these results, for the purpose of organizing the current knowledge and facilitating future research in this area.
Citation: Journal of Algebra and Its Applications
PubDate: 20220319T07:00:00Z
DOI: 10.1142/S021949882350113X

 A characterization of extending trivial Morita contexts

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Authors: S. Moradiani, A. Moussavi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
A right module [math] is extending if every submodule is essential in a direct summand of [math]. In this paper, necessary and sufficient conditions are obtained for a trivial Morita context ring to be right extending.
Citation: Journal of Algebra and Its Applications
PubDate: 20220319T07:00:00Z
DOI: 10.1142/S0219498823501141

 ∗Lietype maps on alternative ∗algebras

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Authors: Aline Jaqueline De Oliveira Andrade, Elisabete Barreiro, Bruno Leonardo Macedo Ferreira
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] and [math] be two alternative ∗algebras with identities [math] and [math], respectively, and [math] and [math] nontrivial symmetric idempotents in [math]. In this paper, we study the characterization of multiplicative ∗Lietype maps. As application, we get a result on alternative [math]algebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20220317T07:00:00Z
DOI: 10.1142/S021949882350130X

 On rings with weak property (A) and their extensions

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Authors: R. K. Sharma, Amit B. Singh
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduce the concept of rings with right (left) weak property (A) which is a generalization of rings with right (left) property (A). A ring [math] has right (left) weak property (A) if every finitely generated twosided ideal [math] of [math] with [math], there exists nonzero [math] [math] such that [math] [math]. Further, we study various extensions of rings with weak property (A) including matrix rings, polynomial rings and Ore extensions.
Citation: Journal of Algebra and Its Applications
PubDate: 20220315T07:00:00Z
DOI: 10.1142/S0219498823501128

 On the Liesolvability of Novikov algebras

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Authors: Kaisar Tulenbaev, Ualbai Umirbaev, Viktor Zhelyabin
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We prove that any Novikov algebra over a field of characteristic [math] is Liesolvable if and only if its commutator ideal [math] is right nilpotent. We also construct examples of infinitedimensional Liesolvable Novikov algebras [math] with nonnilpotent commutator ideal [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220315T07:00:00Z
DOI: 10.1142/S0219498823501177

 Dynamical ideals of noncommutative rings

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Authors: Igor V. Nikolaev
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
A dynamical analog of the prime ideals for simple noncommutative rings is introduced. We prove a factorization theorem for the dynamical ideals. The result is used to classify the surface knots and links in the smooth fourdimensional manifolds.
Citation: Journal of Algebra and Its Applications
PubDate: 20220315T07:00:00Z
DOI: 10.1142/S0219498823501268

 Weak Jordan ∗derivations of prime rings

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Authors: Mohammad Aslam Siddeeque, Nazim Khan, Ali Ahmed Abdullah
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let ∗ be an involution of a noncommutative prime ring [math] with the maximal symmetric ring of quotients and the extended centroid of [math] denoted by [math] and [math], respectively. Consider [math] be an additive map, if [math] for all [math], then such a map [math] is termed as a weak Jordan ∗derivation. With the smart handling of the FItheory and facing the challenging case of low dimensions, we prove that every weak Jordan ∗derivation of [math] is [math]inner unless [math]. Moreover, if ∗ is of the first kind, then every weak Jordan ∗derivation [math] of [math] is [math]inner if and only if [math] is [math]linear.
Citation: Journal of Algebra and Its Applications
PubDate: 20220302T08:00:00Z
DOI: 10.1142/S0219498823501050

 On rings with finite Gorenstein weak global dimension

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Authors: Junpeng Wang, Xiaoxiang Zhang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a ring with finite Gorenstein weak global dimension. We characterize Gorenstein projective, injective and flat modules over [math]. As an application, it is proved that [math] is (strongly) CMfree if and only if [math] has finite weak global dimension.
Citation: Journal of Algebra and Its Applications
PubDate: 20220302T08:00:00Z
DOI: 10.1142/S0219498823501116

 Perfect codes and universal adjacency spectra of commuting graphs of
finite groups
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Authors: Subarsha Banerjee
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The commuting graph [math] of a finite group [math] has vertex set as [math], and any two distinct vertices [math] are adjacent if [math] and [math] commute with each other. In this paper, we first study the perfect codes of [math]. We then find the universal adjacency spectra of the join of two regular graphs, join of two regular graphs in which one graph is a union of two regular graphs, and generalized join of regular graphs in terms of adjacency spectra of the constituent graphs and an auxiliary matrix. As a consequence, we obtain the adjacency, Laplacian, signless Laplacian, and Seidel spectra of the above graph operations. As an application of the results obtained, we calculate the adjacency, Laplacian, signless Laplacian, and Seidel spectra of [math] for [math], where [math] is the dihedral group, [math] is the dicyclic group and [math] is the semidihedral group. Moreover, we provide the exact value of the spectral radius of the adjacency, Laplacian, signless Laplacian, and Seidel matrix of [math] for [math]. Some of the theorems published in [F. Ali and Y. Li, The connectivity and the spectral radius of commuting graphs on certain finite groups, Linear Multilinear Algebra 69 (2019) 1–14; T. Cheng, M. Dehmer, F. EmmertStreib, Y. Li and W. Liu, Properties of commuting graphs over semidihedral groups, Symmetry 13(1) (2021) 103] can be deduced as corollaries from the theorems obtained in this paper.
Citation: Journal of Algebra and Its Applications
PubDate: 20220225T08:00:00Z
DOI: 10.1142/S0219498823500974

 Symbolic defects of edge ideals of unicyclic graphs

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Authors: Mousumi Mandal, Dipak Kumar Pradhan
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We introduce the concept of minimum edge cover for an induced subgraph in a graph. Let [math] be a unicyclic graph with a unique odd cycle and [math] be its edge ideal. We compute the exact values of all symbolic defects of [math] using the concept of minimum edge cover for an induced subgraph in a graph. We describe one method to find the quasipolynomial associated with the symbolic defects of edge ideal [math]. We classify the class of unicyclic graphs when some power of maximal ideal annihilates [math] for any fixed [math]. Also for those class of graphs, we compute the Hilbert function of the module [math] for all [math]
Citation: Journal of Algebra and Its Applications
PubDate: 20220224T08:00:00Z
DOI: 10.1142/S0219498823500998

 Finite groups admitting at most two irreducible characters having equal
codegrees
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Authors: Neda Ahanjideh
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
For a character [math] of a finite group [math], the number [math] is called the codegree of [math]. In this paper, we classify the finite groups in which at most two irreducible characters have equal codegrees.
Citation: Journal of Algebra and Its Applications
PubDate: 20220223T08:00:00Z
DOI: 10.1142/S0219498823500986

 Mixed ∗Jordantype derivations on ∗algebras

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Authors: Bruno Leonardo Macedo Ferreira, Feng Wei
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an ∗algebra with identity [math] and [math] and [math] nontrivial symmetric idempotents in [math]. In this paper we study the characterization of nonlinear mixed ∗Jordantype derivations. In particular, if [math] is a factor von Neumann algebra then every unital nonlinear mixed ∗Jordantype derivations are additive ∗derivations.
Citation: Journal of Algebra and Its Applications
PubDate: 20220223T08:00:00Z
DOI: 10.1142/S0219498823501001

 Generalizations of [math]rings, [math]rings and [math]rings

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Authors: Yiqiang Zhou
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
A unitpicker is a map [math] that associates to every ring [math] a welldefined set [math] of central units in [math] which contains [math], is invariant under isomorphisms of rings, is closed under taking inverses, and which satisfies certain set containment conditions for quotient rings, corner rings and matrix rings. Let [math] be a unitpicker. A ring [math] is called [math] if [math] and [math] if [math] and [math] if [math]. An extensive study of these rings is conducted, and their connections with strongly nil [math]clean rings and semi [math]Boolean rings are investigated. When [math] is specified, known results of [math]rings, [math]rings and [math]rings are obtained and new results are proved.
Citation: Journal of Algebra and Its Applications
PubDate: 20220223T08:00:00Z
DOI: 10.1142/S0219498823501025

 Reflexive ideals and reflexively closed subsets in rings

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Authors: Sera Kim, Tai Keun Kwak, Chang Ik Lee, Yang Lee, Sang Jo Yun
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We continue the study of the reflexivity of ideals, introduced by Mason, and extend this notion to the subsets in rings. We first construct the smallest reflexive ideal containing [math] from any proper ideal [math] of any given ring [math]; by which we can construct reflexive ideals but not semiprime in a kind of noncommutative ring. A subset [math] of a ring [math] is called reflexively closed if [math] for [math] implies [math], checking that a ring [math] is symmetric if and only if the right (left) annihilator of [math] is reflexively closed for any [math]. We prove that the set of all nilpotent elements in a ring [math] is reflexively closed if and only if [math] is nil for any nilpotent element [math] in [math]; and that the Köthe’s conjecture holds if and only if the union (sum) of the upper nilradical and any nil right ideal is reflexively closed. We provide another process to show that the set of all nilpotent elements of the polynomial ring over an NI ring need not be reflexively closed.
Citation: Journal of Algebra and Its Applications
PubDate: 20220223T08:00:00Z
DOI: 10.1142/S0219498823501062

 Multipliers and unicentral diassociative algebras

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Authors: Erik Mainellis
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
This paper details the diassociative analogue of results concerning the Schur multiplier and other extensiontheoretic concepts that originate in group theory. We first prove that covers of diassociative algebras are unique. Second, we show that the multiplier of a diassociative algebra is characterized by the second cohomology group with coefficients in the field. Third, we establish criteria for when the center of a cover maps onto the center of the algebra. Along the way, we obtain a collection of exact sequences, characterizations, and a brief theory of unicentral diassociative algebras and stem extensions. This paper is part of an ongoing project to advance extension theory in the context of several Loday algebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20220223T08:00:00Z
DOI: 10.1142/S0219498823501074

 Discriminant and integral basis of quintic fields defined by [math]

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Authors: Anuj Jakhar, Sumandeep Kaur, Sudesh K. Khanduja
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an algebraic number field with [math] a root of an irreducible trinomial [math] belonging to [math]. In this paper, we compute the highest power of each prime [math] dividing the discriminant of [math] in terms of powers of [math] dividing [math] and the discriminant of [math] besides explicitly constructing a [math]integral basis of [math]. These [math]integral bases lead to the construction of an integral basis of [math] which is illustrated with examples.
Citation: Journal of Algebra and Its Applications
PubDate: 20220223T08:00:00Z
DOI: 10.1142/S0219498823501098

 On prime and primitive ideals of the centrally extended Heisenberg double
of [math]
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Authors: W.Q. Tao
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
For the centrally extended Heisenberg double of [math], a classification of its prime and primitive ideals is obtained. For each primitive ideal, an explicit set of generators is given.
Citation: Journal of Algebra and Its Applications
PubDate: 20220221T08:00:00Z
DOI: 10.1142/S0219498823500962

 A noncommutative Nullstellensatz

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Authors: Zhengheng Bao, Zinovy Reichstein
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a field and [math] be a finitedimensional central division algebra over [math]. We prove a variant of the Nullstellensatz for [math]sided ideals in the ring of polynomial maps [math]. In the case where [math] is commutative, our main result reduces to the [math]Nullstellensatz of Laksov and Adkins–Gianni–Tognoli. In the case, where [math] is the field of real numbers and [math] is the algebra of Hamilton quaternions, it reduces to the quaternionic Nullstellensatz recently proved by Alon and Paran.
Citation: Journal of Algebra and Its Applications
PubDate: 20220217T08:00:00Z
DOI: 10.1142/S0219498823500925

 Units in some group rings over the ring of [math]cyclotomic integers

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Authors: Vitor Araujo Garcia, Raul Antonio Ferraz
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Describing the group of units of a group ring is a classical problem. Let [math] be a rational prime number. We set [math] a primitive root of unity of order [math], [math] the ring of [math]cyclotomic integers, [math] a finite abelian [math]group and [math] the group of the units [math] of [math] such that [math], where [math] is the augmentation map. We will prove that all the elements of the group [math] arise from the units of the group ring [math], where [math] is the cyclic group of order [math]. As an application, we describe explicitly the group of units of the group ring [math] when [math] is an elementary abelian [math]group and [math] is a regular prime number.
Citation: Journal of Algebra and Its Applications
PubDate: 20220217T08:00:00Z
DOI: 10.1142/S0219498823501049

 Axes of Jordan Type in Noncommutative Algebras

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Authors: Louis Rowen, Yoav Segev
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The Peirce decomposition of a Jordan algebra with respect to an idempotent is well known. This decomposition was taken one step further and generalized recently by Hall, Rehren and Shpectorov, with their introduction of axial algebras, and in particular primitive axial algebras of Jordan type (PAJs for short). It turns out that these notions are closely related to threetransposition groups and vertex operator algebras. De Medts, Peacock, Shpectorov and M. Van Couwenberghe generalized axial algebras to decomposition algebras which, in particular, are not necessarily commutative. This paper deals with decomposition algebras which are noncommutative versions of PAJs.
Citation: Journal of Algebra and Its Applications
PubDate: 20220214T08:00:00Z
DOI: 10.1142/S0219498823500949

 Idempotent completion of extriangulated categories

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Authors: Li Wang, Jiaqun Wei, Haicheng Zhang, Tiwei Zhao
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. In this paper, we show that the idempotent completion of an extriangulated category admits a natural extriangulated structure. As an application, we prove that the idempotent completion of a recollement of extriangulated categories is still a recollement.
Citation: Journal of Algebra and Its Applications
PubDate: 20220214T08:00:00Z
DOI: 10.1142/S0219498823500950

 Finite groups with [math]abnormal or [math]subnormal [math]primary
subgroups
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Authors: Muhammad Tanveer Hussain
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be some partition of the set of all primes [math], [math] a finite group and [math]. A set [math] of subgroups of [math] is said to be a complete Hall[math]set of [math] if every nonidentity member of [math] is a Hall [math]subgroup of [math] for some [math] and [math] contains exactly one Hall [math]subgroup of [math] for every [math]. A subgroup [math] of [math] is said to be [math]primary if it is a finite [math]group for some [math]; [math]abnormal in [math] if [math] is not [math]primary whenever [math] and [math] is a maximal subgroup of [math]. A subgroup [math] of [math] is called [math]subnormal if there is a chain of subgroups [math] such that [math] for all [math]. This is equivalent to [math]. In this paper, we study the structure of a finite group [math] in which every [math]primary cyclic subgroups are [math]quasinormal or [math]abnormal. We also describe the structure of a finite group [math] with selfnormalizing or [math]subnormal [math]primary cyclic subgroups for a subgroupclosed saturated lattice formation [math] containing all [math]nilpotent groups.
Citation: Journal of Algebra and Its Applications
PubDate: 20220214T08:00:00Z
DOI: 10.1142/S0219498823501013

 Locally torsionfree modules

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Authors: C. Jayaram, Emel Aslankarayiğit Uğurlu, Ünsal Tekir, Suat Koç
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Recall that a commutative ring [math] is a locally integral domain if its localization [math] is an integral domain for each prime ideal [math] of [math] Our aim in this paper is to extend the notion of locally integral domains to modules. Let [math] be a commutative ring with a unity and [math] a nonzero unital [math]module. [math] is called a locally torsionfree module if the localization [math] of [math] is a torsionfree [math]module for each prime ideal [math] of [math] In addition to giving many properties of locally torsionfree modules, we use them to characterize Baer modules, torsion free modules, and von Neumann regular rings.
Citation: Journal of Algebra and Its Applications
PubDate: 20220214T08:00:00Z
DOI: 10.1142/S0219498823501037

 Einstein nilradicals are completable

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Authors: Lei Zhang, Zaili Yan
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
An Einstein nilradical is a nilpotent Lie algebra which can be the nilradical of an Einstein metric solvable Lie algebra. A Lie algebra is called complete if its center is zero and all its derivations are inner. A nilpotent Lie algebra is called completable if it is the maximal nilpotent ideal of a complete solvable Lie algebra. In this short note, based on the classification result of Einstein metric solvable Lie algebras, we show that any Einstein nilradical is completable. This provides a purely algebraic obstruction for a nilpotent Lie algebra to be an Einstein nilradical.
Citation: Journal of Algebra and Its Applications
PubDate: 20220214T08:00:00Z
DOI: 10.1142/S0219498823501086

 Bisequentially Cohen–Macaulay bipartite graphs

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Authors: Hardi N. Aziz, Amir Mafi, Farnaz Seyfpour
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be the polynomial ring over a field [math], [math] be a graph on vertex set [math] and [math] be its edge ideal. In this paper, we study bisequentially Cohen–Macaulay (biSCM) bipartite graphs and as consequence we classify all biSCM tree graphs. Furthermore, if [math] is biSCM then we determine the projective dimension of [math]. Moreover, we give some examples.
Citation: Journal of Algebra and Its Applications
PubDate: 20220214T08:00:00Z
DOI: 10.1142/S0219498823501104

 On the pronormality of subgroups of odd index in some direct products of
finite groups
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Authors: N. V. Maslova, D. O. Revin
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
A subgroup [math] of a group [math] is said to be pronormal in [math] if [math] and [math] are conjugate in [math] for each [math]. Some problems in Finite Group Theory, Combinatorics and Permutation Group Theory were solved in terms of pronormality, therefore, the question of pronormality of a given subgroup in a given group is of interest. Subgroups of odd index in finite groups satisfy a native necessary condition of pronormality. In this paper, we continue investigations on pronormality of subgroups of odd index and consider the pronormality question for subgroups of odd index in some direct products of finite groups. In particular, in this paper, we prove that the subgroups of odd index are pronormal in the direct product [math] of finite simple symplectic groups over fields of odd characteristics if and only if the subgroups of odd index are pronormal in each direct factor of [math]. Moreover, deciding the pronormality of a given subgroup of odd index in the direct product of simple symplectic groups over fields of odd characteristics is reducible to deciding the pronormality of some subgroup [math] of odd index in a subgroup of [math], where each [math] acts naturally on [math], such that [math] projects onto [math]. Thus, in this paper, we obtain a criterion of pronormality of a subgroup [math] of odd index in a subgroup of [math], where each [math] is a prime and each [math] acts naturally on [math], such that [math] projects onto [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220209T08:00:00Z
DOI: 10.1142/S0219498823500834

 Nonexistence of graded unital homomorphisms between Leavitt algebras and
their Cuntz splices
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Authors: Guido Arnone, Guillermo Cortiñas
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math], let [math] be the graph consisting of one vertex and [math] loops and let [math] be its Cuntz splice. Let [math] and [math] be the Leavitt path algebras over a unital ring [math]. Let [math] be the cyclic group on [math] elements. Equip [math] and [math] with their natural [math]gradings. We show that under mild conditions on [math], which are satisfied, for example, when [math] is a field or a principal ideal domain, there are no unital [math]graded ring homomorphisms [math] nor in the opposite direction.
Citation: Journal of Algebra and Its Applications
PubDate: 20220209T08:00:00Z
DOI: 10.1142/S0219498823500846

 Gerstenhaber algebra of [math]Galois covering of quantum exterior algebra

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Authors: Bo Hou
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be the quantum exterior algebras over a field [math] with [math], [math] be the [math]Galois coverings of [math]. In this paper, a basis of each degree of Hochschild cohomology of [math], the cup product and the Gerstenhaber bracket on Hochschild cohomology of [math] are given.
Citation: Journal of Algebra and Its Applications
PubDate: 20220209T08:00:00Z
DOI: 10.1142/S0219498823500895

 The Schreier property and the composite semigroup ring [math]

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Authors: B. Boulayat, S. El Baghdadi, L. Izelgue
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an extension of integral domains and [math] a commutative, additive, cancellative torsionfree monoid. Let [math] be the semigroup ring of [math] over [math] and set [math]. Suppose that [math]. Then [math] is a subring of [math]. In this paper, we study primal elements in [math] domains. As an application, we characterize when the construction [math] is a (pre)Schreier domain.
Citation: Journal of Algebra and Its Applications
PubDate: 20220204T08:00:00Z
DOI: 10.1142/S0219498823500913

 Flagtransitive quasisymmetric designs with block intersection numbers 0
and 2
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Authors: Wanbao Zhang, Shenglin Zhou
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Quasisymmetric designs are the special type of [math]designs with two block intersection numbers [math] and [math]. In this paper, we study the automorphism groups of quasisymmetric designs with block intersection numbers [math] and [math]. We prove that for a quasisymmetric design [math] with [math] and [math] satisfying that [math] does not divide [math], if [math] is flagtransitive, then [math] must be pointprimitive. We further obtain that [math] is either of affine type or almost simple type by the O’Nan Scott Theorem. Moreover, when the socle of [math] is sporadic, [math] is a unique [math][math] design and [math] or [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220204T08:00:00Z
DOI: 10.1142/S0219498823500937

 Intrinsic entropy for generalized quasimetric semilattices

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Authors: Ilaria Castellano, Dikran Dikranjan, Domenico Freni, Anna Giordano Bruno, Daniele Toller
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We introduce the notion of intrinsic semilattice entropy [math] in the category [math] of generalized quasimetric semilattices and contractive homomorphisms. By using appropriate categories [math] and functors [math], we find specific known entropies [math] on [math] as intrinsic functorial entropies, that is, as [math] F. These entropies are the intrinsic algebraic entropy, the algebraic and the topological entropies for locally linearly compact vector spaces, the topological entropy for totally disconnected locally compact groups and the algebraic entropy for compactly covered locally compact abelian groups.
Citation: Journal of Algebra and Its Applications
PubDate: 20220120T08:00:00Z
DOI: 10.1142/S0219498822502449

 Algebraic properties of face algebras

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Authors: Fabio Calderón, Chelsea Walton
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Prompted by an inquiry of Manin on whether a coacting Hopftype structure [math] and an algebra [math] that is coacted upon share algebraic properties, we study the particular case of [math] being a path algebra [math] of a finite quiver [math] and [math] being Hayashi’s face algebra [math] attached to [math]. This is motivated by the work of Huang, Wicks, Won and the second author, where it was established that the weak bialgebra coacting universally on [math] (either from the left, right, or both sides compatibly) is [math]. For our study, we define the Kronecker square [math] of [math], and show that [math] as unital graded algebras. Then we obtain ringtheoretic and homological properties of [math] in terms of graphtheoretic properties of [math] by way of [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220119T08:00:00Z
DOI: 10.1142/S0219498823500767

 The Jordan–Hölder theorem for monoids with group action

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Authors: Alfilgen Sebandal, Jocelyn Vilela
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we prove an isomorphism theorem for the case of refinement monoids with a group [math] acting on it. Based on this, we show a version of the wellknown Jordan–Hölder theorem in this framework. The central result of this paper states that — as in the case of modules — a monoid [math] has a [math]composition series if and only if it is both [math]Noetherian and [math]Artinian. As in module theory, these two concepts can be defined via ascending and descending chains, respectively.
Citation: Journal of Algebra and Its Applications
PubDate: 20220119T08:00:00Z
DOI: 10.1142/S0219498823500883

 The category [math] of sheaves in [math]

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Authors: Mojgan Mahmoudi, Sara Sepahani
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Since topoi were introduced, there have been efforts putting mathematics into the context of topoi. Amongst known topoi, the topoi of sheaves or presheaves over a small category are of special interest. We have here as the base topos that of sheaves over a monoid [math] as a one object category. By means of closure operators we then obtain categories of sheaves related to the right ideals of [math]. These categories have already been studied but we give these categories a more thorough treatment and reveal some additional properties. Namely, for a weak topology determined by a right ideal [math] of [math], we show that the category of sheaves associated to this topology is a subtopos of [math] (the presheaves over [math]) and determine the Lawvere–Tierney topology yielding the same subtopos, which is the Lawvere–Tierney topology associated to the idempotent hull of the (not necessarily idempotent) closure operator associated to [math]. We will then find conditions under which the subcategory of separated objects turns out to be a topos, and in the last section, we find conditions under which the category of sheaves becomes a De Morgan topos.
Citation: Journal of Algebra and Its Applications
PubDate: 20220115T08:00:00Z
DOI: 10.1142/S0219498823500858

 Special clean elements, perspective elements and perspective rings

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Authors: Xavier Mary
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Motivated by the idea of perspectivity of rings and modules, we introduce perspective elements of a ring. We notably prove that perspective elements form a proper subset of special clean elements, and that perspectivity of elements is a leftright symmetric property. An equational characterization of perspective elements is also given and examples are provided.
Citation: Journal of Algebra and Its Applications
PubDate: 20220115T08:00:00Z
DOI: 10.1142/S0219498823500901

 On [math]torsion exact sequences and [math]projective modules ([math])

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Authors: Wei Zhao, Yongyan Pu, Mingzhao Chen, Xuelian Xiao
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative ring and [math] a given multiplicative closed subset of [math]. In this paper, we introduce the new concept of [math]torsion exact sequences (respectively, [math]torsion commutative diagrams) as a generalization of exact sequences (respectively, commutative diagrams). As an application, they can be used to characterize two classes of modules that are generalizations of projective modules.
Citation: Journal of Algebra and Its Applications
PubDate: 20220112T08:00:00Z
DOI: 10.1142/S021949882350086X

 A bicategorical approach to actions of monoidal categories

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Authors: Bojana Femić
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We characterize in bicategorical terms actions of monoidal categories on the categories of representations of algebras and of relative Hopf modules. For this purpose we introduce 2cocycles in any 2category [math]. We observe that under certain conditions the structures of pseudofunctors between bicategories are in onetoone correspondence with (twisted) 2cocycles in the image bicategory. In particular, for certain pseudofunctors to Cat, the 2category of categories, one gets 2cocycles in the free completion 2category under Eilenberg–Moore objects, constructed by Lack and Street. We introduce (co)quasibimonads in [math] and a suitable bicategory of Tambara (co)modules over (co)quasibimonads in [math] fitting the setting of the latter pseudofuntors. We describe explicitly the involved 2cocycles in this context and show how they are related to Sweedler’s and Hausser–Nill 2cocycles in [math], which we define. This allows us to recover some results of Schauenburg, Balan, Hausser and Nill for modules over commutative rings. We fit a version of the 2category of bimonads in [math], which we introduced in a previous paper, in a similar setting as above and recover a result of Laugwitz. We observe that pseudofunctors to Cat in general determine what we call pseudoactions of homcategories, which correspond to the whole range of a 2cocycle, so that the described actions of categories appear as restrictions of these 2cocycles to endohom categories.
Citation: Journal of Algebra and Its Applications
PubDate: 20220111T08:00:00Z
DOI: 10.1142/S0219498823500731

 Differential equations defined by (convergent) Laurent series

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Authors: Vakhtang Lomadze
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The class of ordinary linear constant coefficient differential equations is naturally embedded into a wider class by associating differential equations to (convergent) Laurent series. It is thought that these more general differential equations can be used as an alternative description of some special functions.
Citation: Journal of Algebra and Its Applications
PubDate: 20220110T08:00:00Z
DOI: 10.1142/S0219498823500871

 Finite generation of the cohomology rings for the extension algebras of
monomial algebras
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Authors: Hongbo Shi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We describe the cohomology ring of a monomial algebra in the language of dimension tree or minimal resolution graph and in this context we study the finite generation of the cohomology rings of the extension algebras, showing among others that the cohomology ring [math] is finitely generated [math] is [math] is, where [math] is the dual extension of a monomial algebra [math] and [math] is the opposite algebra of [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20220107T08:00:00Z
DOI: 10.1142/S0219498823500718

 Finite [math]groups

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Authors: Dandan Zhang, Haipeng Qu, Yanfeng Luo
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a group and [math]. [math] is said to be a [math]group if [math] is a chain under set inclusion. In this paper, we prove that a finite [math]group is a semidirect product of a Sylow [math]subgroup and an abelian [math]subgroup. For the case of [math] being a finite [math]group, we obtain an optimal upper bound of [math] for a [math] [math]group [math]. We also prove that a [math] [math]group is metabelian when [math] and provide an example showing that a nonabelian [math] [math]group is not necessarily metabelian when [math]. In particular, [math] [math]groups are characterized.
Citation: Journal of Algebra and Its Applications
PubDate: 20220107T08:00:00Z
DOI: 10.1142/S0219498823500755

 Factorization invariants of the additive structure of exponential Puiseux
semirings
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Authors: Harold Polo
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Exponential Puiseux semirings are additive submonoids of [math] generated by almost all of the nonnegative powers of a positive rational number, and they are natural generalizations of rational cyclic semirings. In this paper, we investigate some of the factorization invariants of exponential Puiseux semirings and briefly explore the connections of these properties with semigrouptheoretical invariants. Specifically, we provide exact formulas to compute the catenary degrees of these monoids and show that minima and maxima of their sets of distances are always attained at Betti elements. Additionally, we prove that sets of lengths of atomic exponential Puiseux semirings are almost arithmetic progressions with a common bound, while unions of sets of lengths are arithmetic progressions. We conclude by providing various characterizations of the atomic exponential Puiseux semirings with finite omega functions; in particular, we completely describe them in terms of their presentations.
Citation: Journal of Algebra and Its Applications
PubDate: 20220107T08:00:00Z
DOI: 10.1142/S0219498823500779

 On the reduction numbers and the Castelnuovo–Mumford regularity of
projective monomial curves
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Authors: Tran Thi Gia Lam
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
This paper gives explicit formulas for the reduction number and the Castelnuovo–Mumford regularity of projective monomial curves.
Citation: Journal of Algebra and Its Applications
PubDate: 20220107T08:00:00Z
DOI: 10.1142/S0219498823500822

 Holomorphic integer graded vertex superalgebras

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Authors: Jethro van Ekeren, Bely Rodríguez Morales
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we study holomorphic [math]graded vertex superalgebras. We prove that all such vertex superalgebras of central charge [math] and [math] are purely even. For the case of central charge [math] we prove that the weightone Lie superalgebra is either zero, of superdimension [math], or else is one of an explicit list of 1332 semisimple Lie superalgebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20211231T08:00:00Z
DOI: 10.1142/S0219498823500810

 On the notion of supplement in acts over monoids

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Authors: B. Tahmasebi Ashtiani, H. Rasouli, A. Tehranian, H. Barzegar
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The object of this paper is to generalize the notion of supplement in modules to monoid acts. In contrast to the case of modules that supplements of submodules do not generally exist, here we uniquely characterize the supplement of a proper subact of an act. Supplemented acts are defined as acts whose proper subacts all have proper supplements. We discuss how the property of being supplemented relates to certain other properties of acts. In particular, we prove that being supplemented and being completely reducible coincide.
Citation: Journal of Algebra and Its Applications
PubDate: 20211230T08:00:00Z
DOI: 10.1142/S0219498823500664

 Rings with [math]acc on [math]annihilators

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Authors: Ahmed Hamed, Achraf Malek, Ridha Chatbouri
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
A commutative ring [math] is said to satisfy acc on dannihilators if for every sequence [math] of elements of [math] the sequence [math] is stationary. In this paper we extend the notion of rings with acc on dannihilators by introducing the concept of rings with [math]acc on dannihilators, where [math] is a multiplicative set. Let [math] be a commutative ring and [math] a multiplicative subset of [math] We say that [math] satisfies [math]acc on dannihilators if for every sequence [math] of elements of [math] the sequence [math] is [math]stationary, that is, there exist a positive integer [math] and an [math] such that for each [math] [math] We give equivalent conditions for the power series (respectively, polynomial) ring over an Armendariz ring to satisfy [math]acc on dannihilators. We also study serval properties of rings satisfying [math]acc on dannihilators. The concept of the amalgamated duplication of [math] along an ideal [math] [math] is studied.
Citation: Journal of Algebra and Its Applications
PubDate: 20211230T08:00:00Z
DOI: 10.1142/S0219498823500706

 Invertible matrices over a class of semirings

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Authors: David Dolžan
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We characterize the invertible matrices over a class of semirings such that the set of additively invertible elements is equal to the set of nilpotent elements. We achieve this by studying the liftings of the orthogonal sums of elements that are “almost idempotent” to those that are idempotent. Finally, we show an application of the obtained results to calculate the diameter of the commuting graph of the group of invertible matrices over the semirings in question.
Citation: Journal of Algebra and Its Applications
PubDate: 20211230T08:00:00Z
DOI: 10.1142/S0219498823500792

 Classification of graded cluster algebras generated by rank 3 quivers

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Authors: Thomas BookerPrice
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We consider gradings on cluster algebras generated by [math] skewsymmetric matrices. We show that, except in one particular case, mutationcyclic matrices give rise to gradings in which all occurring degrees are positive and have only finitely many associated cluster variables. For mutationacyclic matrices, we prove that all occurring degrees are associated with infinitely many variables. We also give a direct proof that the gradings are balanced in this case (i.e. that there is a bijection between the cluster variables of degree [math] and [math] for each occurring degree [math]).
Citation: Journal of Algebra and Its Applications
PubDate: 20211228T08:00:00Z
DOI: 10.1142/S0219498823500354

 Finite groups with a nilpotency condition

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Authors: Hassan Khosravi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] and [math] be positive integer numbers. In this paper, we study [math], the class of all groups [math] that for all subsets [math] and [math] of [math] containing [math] and [math] elements, respectively, there exist [math] and [math] such that [math] is nilpotent, which introduced by Zarrin in 2012. We improve some results of Zarrin and find some sharp bounds for [math] and [math] such that [math] implies that [math] is nilpotent. Also we will characterize all finite [math]groups in [math], which [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211228T08:00:00Z
DOI: 10.1142/S021949882350072X

 New characterizations of [math]coherent rings

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Authors: Wei Qi, Xiaolei Zhang, Wei Zhao
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduce and study the class [math][math]ML of [math]MittagLeffler modules with respect to all flat modules. We show that a ring [math] is [math]coherent if and only if every ideal is in [math][math]ML, if and only if [math][math]ML is closed under submodules. As an application, we obtain the [math]version of Chase Theorem: a ring [math] is [math]coherent if and only if any direct product of copies of [math] is [math]flat, if and only if any direct product of flat [math]modules is [math]flat. Consequently, we provide an answer to the open question proposed by Bennis and El Hajoui [On [math]coherence, J. Korean Math. Soc. 55(6) (2018) 1499–1512].
Citation: Journal of Algebra and Its Applications
PubDate: 20211228T08:00:00Z
DOI: 10.1142/S0219498823500780

 On the regularity of product of irreducible monomial ideals

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Authors: Yubin Gao
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a polynomial ring in [math] variables over a field [math]. When [math], [math] and [math] are monomial ideals of [math] generated by powers of the variables [math], it is proved that [math]. If [math], the same result for the product of a finite number of ideals as above is proved.
Citation: Journal of Algebra and Its Applications
PubDate: 20211228T08:00:00Z
DOI: 10.1142/S0219498823500809

 Triangular matrix coalgebras: Representation theory and recollement

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Authors: Xuerong Fu, Hailou Yao, Yonggang Hu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
For any triangular matrix coalgebra [math], in this paper, we first examine some connections between coalgebra properties of [math] and its constituent coalgebras [math], [math], which contain semiperfectness, computability and row/columnfiniteness of their left Cartan matices. Then we devote to considering the coresolution dimensions of recollement of comodule categories by investigating covariantly finite subcategories.
Citation: Journal of Algebra and Its Applications
PubDate: 20211224T08:00:00Z
DOI: 10.1142/S0219498823500421

 The unitary subgroups of group algebras of a class of finite [math]groups

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Authors: Yulei Wang, Heguo Liu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a prime and let [math] be a finite field of characteristic [math]. Let [math] denote the group algebra of the finite [math]group [math] over the field [math] and let [math] denote the group of normalized units in [math]. The antiautomorphism [math] of [math] extends linearly to an antiautomorphism [math] of [math]. An element [math] is called unitary if [math]. All unitary elements of [math] form a subgroup which is denoted by [math]. If [math] is odd, the order of [math] is [math]. However, to compute the order of [math] still is open when [math]. In this paper, the order of [math] is computed when [math] is a nonabelian [math]group given by a central extension of the following form: 1 → ℤ2m → G → ℤ2 ×⋯ × ℤ2 → 1 and [math], [math]. Further, a conjecture is confirmed, namely, the order of [math] can be divided by [math], where [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211224T08:00:00Z
DOI: 10.1142/S0219498823500433

 On 2absorbing ideals of commutative semirings

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Authors: Leena Sawalmeh, Mohammed Saleh
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative semiring with unity different than zero. In this paper, we study the concept of [math]absorbing ideals of [math] which can be considered as a generalization of prime ideals. Among others, it is shown that the radical of a [math]absorbing ideal is also a [math]absorbing ideal and there are at most [math] prime [math]ideals of [math] that are minimal over a [math]absorbing ideals.
Citation: Journal of Algebra and Its Applications
PubDate: 20211223T08:00:00Z
DOI: 10.1142/S0219498823500639

 Limit behavior of the rational powers of monomial ideals

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Authors: James Lewis
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We investigate the rational powers of ideals. We find that in the case of monomial ideals, the canonical indexing leads to a characterization of the rational powers yielding that symbolic powers of squarefree monomial ideals are indeed rational powers themselves. Using the connection with symbolic powers techniques, we use splittings to show the convergence of depths and normalized Castelnuovo–Mumford regularities. We show the convergence of Stanley depths for rational powers, and as a consequence of this, we show the beforenow unknown convergence of Stanley depths of integral closure powers. Additionally, we show the finiteness of asymptotic associated primes, and we find that the normalized lengths of local cohomology modules converge for rational powers, and hence for symbolic powers of squarefree monomial ideals.
Citation: Journal of Algebra and Its Applications
PubDate: 20211223T08:00:00Z
DOI: 10.1142/S021949882350069X

 The subclass sizes of some elements being square free

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Authors: Xianhe Zhao, Yanyan Zhou, Ruifang Chen, Qin Huang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an element of a finite group [math], and [math] a prime factor of the order of [math]. It is clear that there always exists a unique minimal subnormal subgroup containing [math], say [math]. We call the conjugacy class of [math] in [math] the subclass of [math] in [math], see [G. Qian and Y. Yang, On subclass sizes of finite groups, J. Aust. Math. Soc. (2020) 402–411]. In this paper, assume that [math] is the product of the subgroups [math] and [math], we investigate the solvability, [math]nilpotence and supersolvability of the group [math] under the condition that the subclass sizes of prime power order elements in [math] are [math] free, [math] free and square free, respectively, so that some known results relevant to conjugacy class sizes are generalized.
Citation: Journal of Algebra and Its Applications
PubDate: 20211223T08:00:00Z
DOI: 10.1142/S0219498823500743

 Some generalizations of Shao and Beltrán’s theorem

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Authors: Minghui Li, Jiakuan Lu, Boru Zhang, Wei Meng
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] and [math] be finite groups of relative coprime orders and [math] act on [math] via automorphisms. In this paper, we prove that when every maximal [math]invariant subgroup of [math] that contains the normalizer of some Sylow subgroup has prime index, then [math] is supersolvable; if every nonnilpotent maximal [math]invariant subgroup of [math] has prime index or is normal in [math], then [math] is a Sylow tower group.
Citation: Journal of Algebra and Its Applications
PubDate: 20211222T08:00:00Z
DOI: 10.1142/S0219498823500676

 A study of a family of monomial ideals

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Authors: J. William Hoffman, Haohao Wang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we study a family of rational monomial parametrizations. We investigate a few structural properties related to the corresponding monomial ideal [math] generated by the parametrization. We first find the implicit equation of the closure of the image of the parametrization. Then we provide a minimal graded free resolution of the monomial ideal [math], and describe the minimal graded free resolution of the symmetric algebra of [math]. Finally, we provide a method to compute the defining equations of the Rees algebra of [math] using three moving planes that follow the parametrization.
Citation: Journal of Algebra and Its Applications
PubDate: 20211222T08:00:00Z
DOI: 10.1142/S0219498823500688

 On the lengths of group algebras of finite abelian groups in the
semisimple case
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Authors: Alexander Guterman, Olga Markova, Mikhail Khrystik
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper we solve the problem of finding the length of group algebras of arbitrary finite abelian groups in the case when the characteristic of the ground field does not divide the order of the group. We show that these group algebras have maximal possible lengths for infinite fields and sufficiently large finite fields since they are onegenerated. In case of small fields we prove that the length is bounded from above by a logarithmic function of the order of the group.
Citation: Journal of Algebra and Its Applications
PubDate: 20211213T08:00:00Z
DOI: 10.1142/S0219498822501407

 A characterization of graded pseudovaluation domains

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Authors: Malik Tusif Ahmed, Chahrazade Bakkari, Najib Mahdou, Abdelkbir Riffi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a torsionless grading monoid, [math] a [math]graded integral domain, [math] the set of nonzero homogeneous elements of [math], [math] the quotient field of [math] and [math] the group of units of [math]. We say that [math] is a graded pseudovaluation domain (grPVD) if whenever a homogeneous prime ideal [math] of [math] contains the product [math] of two homogeneous elements of [math], then [math] or [math]. The notion of grPVDs was introduced recently by the authors in (M. T. Ahmed, C. Bakkari, N. Mahdou and A. Riffi, Graded pseudovaluation domains, Comm. Algebra 48 (2020) 4555–4568) as a graded version of pseudovaluation domains (PVDs). In this paper, we show that [math] is a grPVD if and only if exactly one of the following two conditions holds: (1) (a)[math], (b)[math] is a pseudovaluation monoid, and (c)[math] for every [math] whenever [math] is not a unit. (2) (a)[math], (b)[math] is a valuation monoid, (c)[math] for every [math] whenever [math] is not a unit, and (d)[math] is a grPVD.
Citation: Journal of Algebra and Its Applications
PubDate: 20211209T08:00:00Z
DOI: 10.1142/S0219498823500445

 Representations and deformations of 3Hom[math]Lie algebras

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Authors: Esmaeil Peyghan, Aydin Gezer, Zahra Bagheri, Inci Gultekin
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The aim of this paper is to introduce 3Hom[math]Lie algebra structures generalizing the algebras of 3HomLie algebra. Also, we investigate the representations and deformations theory of this type of HomLie algebras. Moreover, we introduce the definition of extensions and abelian extensions of 3Hom[math]Lie algebras and show that associated to any abelian extension, there is a representation and a 2cocycle.
Citation: Journal of Algebra and Its Applications
PubDate: 20211209T08:00:00Z
DOI: 10.1142/S0219498823500640

 Poisson algebra structure on the invariants of pairs of matrices of degree
three
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Authors: Z. Normatov, R. Turdibaev
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We provide a table of multiplication of the Poisson algebra on the minimal set of generators of the invariants of pairs of matrices of degree three.
Citation: Journal of Algebra and Its Applications
PubDate: 20211209T08:00:00Z
DOI: 10.1142/S0219498823500652

 Ideal factorization in strongly discrete independent rings of Krull type

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Authors: Gyu Whan Chang, Hyun Seung Choi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an integral domain and [math] be the socalled [math]operation on [math]. In this paper, we define the notion of [math]ZPUI domains which is a natural generalization of ZPUI domains introduced by Olberding in 2000. We say that [math] is a [math]ZPUI domain if every nonzero proper [math]ideal [math] of [math] can be written as [math] for some [math]invertible ideal [math] of [math] and [math] is a nonempty collection of pairwise [math]comaximal prime [math]ideals of [math]. Then, among other things, we show that [math] is a [math]ZPUI domain if and only if the polynomial ring [math] is a [math]ZPUI domain, if and only if [math] is a strongly discrete independent ring of Krull type. We construct three types of new [math]ZPUI domains from an old one by [math]construction, pullback, and [math]domains. We also show that given an abelian group [math], there is a ZPUI domain with ideal class group [math] but not a Dedekind domain. Finally, we introduce and study the notion of [math]ISP domains as a generalization of [math]ZPUI domains.
Citation: Journal of Algebra and Its Applications
PubDate: 20211204T08:00:00Z
DOI: 10.1142/S0219498823500457

 Graded 1absorbing prime ideals of graded commutative rings

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Authors: Mohammed Issoual
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a group with identity [math] and [math] be [math]graded commutative ring with [math] In this paper, we introduce and study the graded versions of 1absorbing prime ideal. We give some properties and characterizations of these ideals in graded ring, and we give a characterization of graded 1absorbing ideal the idealization [math]
Citation: Journal of Algebra and Its Applications
PubDate: 20211204T08:00:00Z
DOI: 10.1142/S0219498823500585

 Primality of closed path polyominoes

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Authors: Carmelo Cisto, Francesco Navarra
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduce a new class of polyominoes, called closed paths, and we study the primality of their associated ideal. Inspired by an existing conjecture that characterizes the primality of a polyomino ideal by nonexistence of zigzag walks, we classify all closed paths which do not contain zigzag walks, and we give opportune toric representations of the associated ideals. To support the conjecture, we prove that having no zigzag walks is a necessary and sufficient condition for the primality of the associated ideal of a closed path. Finally, we present some classes of prime polyominoes viewed as generalizations of closed paths.
Citation: Journal of Algebra and Its Applications
PubDate: 20211202T08:00:00Z
DOI: 10.1142/S021949882350055X

 Flat commutative ring epimorphisms of almost Krull dimension zero

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Authors: Leonid Positselski
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we consider flat epimorphisms of commutative rings [math] such that, for every ideal [math] for which [math], the quotient ring [math] is semilocal of Krull dimension zero. Under these assumptions, we show that the projective dimension of the [math]module [math] does not exceed [math]. We also describe the Geigle–Lenzing perpendicular subcategory [math] in [math]. Assuming additionally that the ring [math] and all the rings [math] are perfect, we show that all flat [math]modules are [math]strongly flat. Thus, we obtain a generalization of some results of the paper [6], where the case of the localization [math] of the ring [math] at a multiplicative subset [math] was considered.
Citation: Journal of Algebra and Its Applications
PubDate: 20211202T08:00:00Z
DOI: 10.1142/S0219498823500603

 Fibonacci length and the generalized order kPell sequences of the
2generator pgroups of nilpotency class 2
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Authors: E. Mehraban, M. Hashemi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we consider the 2generator pgroups of nilpotency class 2. We find the Fibonacci length and the period of the generalized order kPell sequences of these groups.
Citation: Journal of Algebra and Its Applications
PubDate: 20211202T08:00:00Z
DOI: 10.1142/S0219498823500615

 Skew [math]codes

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Authors: S. T. Dougherty, Serap Şahinkaya, Bahattin Yıldız
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We describe skew [math]codes, which are codes that are the ideals in a skew group ring, where the ring is a finite commutative Frobenius ring and [math] is an arbitrary finite group. These codes generalize many of the wellknown classes of codes such as cyclic, quasicyclic, constacyclic codes, skew cyclic, skew quasicyclic and skew constacyclic codes. Additionally, using the skew [math]matrices, we can generalize almost all the known constructions in the literature for selfdual codes.
Citation: Journal of Algebra and Its Applications
PubDate: 20211130T08:00:00Z
DOI: 10.1142/S0219498823500561

 On Posner’s theorem with [math]generalized skew derivations on Lie
ideals
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Authors: Luisa Carini, Giovanni Scudo
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a noncommutative prime ring of characteristic different from [math] and [math], [math] its right Martindale quotient ring and [math] its extended centroid. Suppose that [math] is a noncentral Lie ideal of [math], [math] a nonzero [math]generalized skew derivation of [math]. If [[F(x),x],F(x)] ∈ Z(R), for all [math], then one of the following holds: (a)there exists [math] such that [math], for all [math]; (b)[math], the ring of [math] matrices over [math], and there exist [math] and [math] such that [math], for all [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211130T08:00:00Z
DOI: 10.1142/S0219498823500573

 [math]algebras and topology

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Authors: Wolfgang Rump
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
[math]algebras are based on an equation which is fundamental in the construction of various torsionfree groups, including spherical Artin groups, Riesz groups, certain mapping class groups, paraunitary groups, and structure groups of settheoretic solutions to the Yang–Baxter equation. A topological study of [math]algebras is initiated. A prime spectrum is associated to certain (possibly all) [math]algebras, including three classes of [math]algebras where the ideals are determined in a more explicite fashion. Known results on orthomodular lattices, Heyting algebras, or quantales are extended and revisited from an [math]algebraic perspective.
Citation: Journal of Algebra and Its Applications
PubDate: 20211127T08:00:00Z
DOI: 10.1142/S0219498823500342

 A necessary condition for discrete branching laws for Klein four symmetric
pairs
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Authors: Haian He
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We show a necessary condition for Klein four symmetric pairs [math] satisfying the condition (D.D.); that is, there exists at least one infinitedimensional simple [math]module that is discretely decomposable as a [math]module. This work is a continuation of [A criterion for discrete branching laws for Klein four symmetric pairs and its application to [math], Int. J. Math. 31(6) (2020) 2050049]. Moreover, we define associated Klein four symmetric pairs, and we may use these tools to compute that a class of Klein four symmetric pairs do not satisfy the condition (D.D.); for example, [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211127T08:00:00Z
DOI: 10.1142/S0219498823500391

 Nonlinear Lie triple derivations by local actions on triangular algebras

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Authors: Xingpeng Zhao
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a triangular algebra over a commutative ring [math]. In this paper, under some mild conditions on [math], we prove that if [math] is a nonlinear map satisfying δ([[U,V ],W]) = [[δ(U),V ],W] + [[U,δ(V )],W] + [[U,V ],δ(W)] for any [math] with [math]. Then [math] is almost additive on [math], that is, δ(U + V ) − δ(U) − δ(V ) ∈ð’µ(ð’°). Moreover, there exist an additive derivation [math] of [math] and a nonlinear map [math] such that [math] for [math], where [math] for any [math] with [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211127T08:00:00Z
DOI: 10.1142/S0219498823500597

 Distributive Noetherian centrally essential rings

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Authors: V. T. Markov, A. A. Tuganbaev
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
It is proved that a ring [math] is a right or left Noetherian, right distributive, centrally essential ring if and only if [math], where each of the rings [math] is either a commutative Dedekind domain or a left and right Artinian, left and right uniserial ring.
Citation: Journal of Algebra and Its Applications
PubDate: 20211126T08:00:00Z
DOI: 10.1142/S0219498823500627

 Feedback linearly extended discrete functions

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Authors: Claude Gravel, Daniel Panario
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we study a new flexible method to extend linearly the graph of a nonlinear, and usually not bijective, function so that the resulting extension is a bijection. Our motivation comes from cryptography. Examples from symmetric cryptography are given as how the extension was used implicitly in the construction of some wellknown block ciphers. The method heavily relies on ideas brought from linear coding theory and secret sharing. We are interested in the behavior of the composition of many extensions, and especially the space of parameters that defines a family of equations based on finite differences or linear forms. For any linear extension, we characterize entirely the space of parameters for which such equations are solvable in terms of the space of parameters that render those equations for the corresponding nonlinear extended functions solvable. Conditions are derived to assess the solvability of those kind of equations in terms of the number of compositions or iterations. We prove a relation between the number of compositions and the dimensions of vector spaces that appear in our results. The proofs of those properties rely mostly on tools from linear algebra.
Citation: Journal of Algebra and Its Applications
PubDate: 20211124T08:00:00Z
DOI: 10.1142/S0219498823500512

 Cancellation properties of graded and nonunital rings. Graded clean and
graded exchange Leavitt path algebras
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Authors: Lia Vaš
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Various authors have been generalizing some unital ring properties to nonunital rings. We consider properties related to cancellation of modules (being unitregular, having stable range one, being directly finite, exchange, or clean) and their “local” versions. We explore their relationships and extend the defined concepts to graded rings. With graded clean and graded exchange rings suitably defined, we study how these properties behave under the formation of graded matrix rings. We exhibit properties of a graph [math] which are equivalent to the unital Leavitt path algebra [math] being graded clean. We also exhibit some graph properties which are necessary and some which are sufficient for [math] to be graded exchange.
Citation: Journal of Algebra and Its Applications
PubDate: 20211122T08:00:00Z
DOI: 10.1142/S0219498823500500

 Metrizability of spaces of valuation domains associated to
pseudoconvergent sequences
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Authors: G. Peruginelli, D. Spirito
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a valuation domain of rank one with quotient field [math]. We study the set of extensions of [math] to the field of rational functions [math] induced by pseudoconvergent sequences of [math] from a topological point of view, endowing this set either with the Zariski or with the constructible topology. In particular, we consider the two subspaces induced by sequences with a prescribed breadth or with a prescribed pseudolimit. We give some necessary conditions for the Zariski space to be metrizable (under the constructible topology) in terms of the value group and the residue field of [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211117T08:00:00Z
DOI: 10.1142/S0219498823500469

 Symmetric polynomials in the free metabelian Poisson algebras

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Authors: Andre Dushimirimana, Şehmus Fındık, Nazar Şahi̇n Öğüşlü
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a field of characteristic zero and [math] be a finite set of variables. Consider the free metabelian Poisson algebra [math] of rank [math] generated by [math] over [math]. An element in [math] is called symmetric if it is preserved under any change of variables, i.e. under the action of each permutation in [math]. In this study, we determine the algebra [math] of symmetric polynomials of [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211117T08:00:00Z
DOI: 10.1142/S0219498823500494

 The Valabrega–Valla module of monomial ideals

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Authors: Abbas Nasrollah Nejad, Ali Akbar Yazdan Pour
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we focus on the initial degree and the vanishing of the Valabrega–Valla module of a pair of monomial ideals [math] in a polynomial ring over a field [math]. We prove that the initial degree of this module is bounded above by the maximum degree of a minimal generators of [math]. For edge ideal of graphs, a complete characterization of the vanishing of the Valabrega–Valla module is given. For higher degree ideals, we find classes, where the Valabrega–Valla module vanishes. For the case that [math] is the facet ideal of a clutter [math] and [math] is the defining ideal of singular subscheme of [math], the nonvanishing of this module is investigated in terms of the combinatorics of [math]. Finally, we describe the defining ideal of the Rees algebra of [math] provided that the Valabrega–Valla module is zero.
Citation: Journal of Algebra and Its Applications
PubDate: 20211117T08:00:00Z
DOI: 10.1142/S0219498823500536

 Domains whose ideals meet a universal restriction

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Authors: Muhammad Zafrullah
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] represent a set of proper nonzero ideals [math] (respectively, [math]ideals [math]) of an integral domain [math] and let [math] be a valid property of ideals of [math] We say [math] meets [math] (denoted [math] if each [math] is contained in an ideal satisfying [math]. If [math] [math] [math] cannot be controlled. When [math] [math] [math] does not imply [math] [math] while [math] [math] implies [math] [math] usually. We say [math] meets [math] with a twist [math]written [math] if each [math] is such that, for some [math] [math] is contained in an ideal satisfying [math] and study [math] as its predecessor. A modification of the above approach is used to give generalizations of almost bezout domains.
Citation: Journal of Algebra and Its Applications
PubDate: 20211113T08:00:00Z
DOI: 10.1142/S0219498823500408

 Ramification structures for quotients of the Grigorchuk groups

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Authors: Marialaura Noce, Anitha Thillaisundaram
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Groups associated to surfaces isogenous to a higher product of curves can be characterized by a purely grouptheoretic condition, which is the existence of the socalled ramification structure. In this paper, we prove that infinitely many quotients of the Grigorchuk groups admit ramification structures. This gives the first explicit infinite family of 3generated finite 2groups with ramification structures.
Citation: Journal of Algebra and Its Applications
PubDate: 20211113T08:00:00Z
DOI: 10.1142/S0219498823500470

 Invariant bilinear operators and the second [math]relative cohomology of
the Lie algebra of vector fields on [math]
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Authors: Meher Abdaoui
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be the Lie algebra of smooth vector fields on [math] and [math] be the space of bilinear differential operators acting on weighted densities. In this paper, we classify [math]invariant skewsymmetric binary differential operators from [math] to [math] vanishing on [math]. This result allows us to compute the second differential [math]relative cohomology of [math] with coefficients in [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211113T08:00:00Z
DOI: 10.1142/S0219498823500524

 On weakly [math]semipermutable subgroups of finite groups

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Authors: Venus Amjid, Muhammad Tanveer Hussain, Zhenfeng Wu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be some partition of the set of all primes [math], [math] be a finite group and [math]. A set [math] of subgroups of [math] is said to be a complete Hall[math]set of [math] if every nonidentity member of [math] is a Hall [math]subgroup of [math] for some [math] and [math] contains exactly one Hall [math]subgroup of [math] for every [math]. Let [math] be a complete Hall [math]set of [math]. A subgroup [math] of [math] is said to be [math]semipermutable with respect to [math] if [math] for all [math] and all [math] such that [math]; [math]semipermutablein [math] if [math] is [math]semipermutable in [math] with respect to some complete Hall [math]set of [math]. We say that a subgroup [math] of [math] is weakly[math]semipermutable in [math] if there exists a [math]permutable subgroup [math] of [math] such that [math] is [math]permutable in [math] and [math], where [math] is the subgroup of [math] generated by all those subgroups of [math] which are [math]semipermutable in [math]. In this paper, we study the structure of [math] under the condition that some subgroups of [math] are weakly [math]semipermutable in [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211111T08:00:00Z
DOI: 10.1142/S0219498823500482

 On the Galois symmetries for the character table of an integral fusion
category
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Authors: Sebastian Burciu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we show that integral fusion categories with rational structure constants admit a natural group of symmetries given by the Galois group of their character tables. Based on these symmetries, we generalize a wellknown result of Burnside from representation theory of finite groups. More precisely, we show that any row corresponding to a noninvertible object in the character table of a weakly integral fusion category contains a zero entry.
Citation: Journal of Algebra and Its Applications
PubDate: 20211106T07:00:00Z
DOI: 10.1142/S0219498823500263

 On classical [math]prime subsemimodules

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Authors: M. J. Nikmehr, R. Nikandish, A. Yassine
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduce the notion of classical [math]prime subsemimodules of a semimodule [math] over a commutative semiring [math] with identity, which is a generalization of classical prime subsemimodules. A proper subsemimodule [math] of [math] having the property that for each [math] and each subsemimodule [math] of [math], the inclusion [math] implies [math] or [math] is called classical [math]prime. We give some results concerning classical [math]prime subsemimodules. Also, the classical [math]prime avoidance theorem for subsemimodules is proved. Finally, the notion of valuation semimodules is introduced and some results on classical [math]prime subsemimodules in valuation semimodules are given.
Citation: Journal of Algebra and Its Applications
PubDate: 20211106T07:00:00Z
DOI: 10.1142/S021949882350041X

 On [math]supplemented subgroups of some sylow subgroups of finite groups

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Authors: Xuanli He, Qinghong Guo, Muhong Huang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a finite group. A subgroup [math] of [math] is called to be [math]permutable in [math] if [math] permutes with all Sylow subgroups of [math]. A subgroup [math] of [math] is said to be [math]supplemented in [math] if there exists a subgroup [math] of [math] such that [math] and [math] is [math]permutable in [math]. In this paper, we investigate [math]nilpotency of a finite group. As applications, we give some sufficient and necessary conditions for a finite group belongs to a saturated formation.
Citation: Journal of Algebra and Its Applications
PubDate: 20211030T07:00:00Z
DOI: 10.1142/S0219498823500275

 Generalized [math]derivations on prime rings

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Authors: V. De Filippis, S.K. Tiwari, Sanjay Kumar Singh
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We introduce the definitions of [math]derivations and generalized [math]derivations on a ring [math]. The main objective of the paper is to describe the structure of a prime ring [math] in which [math]derivations and generalized [math]derivations satisfy certain algebraic identities with involution ⋆, antiautomorphism and automorphism. Some wellknown results concerning derivations, generalized derivations, skew derivations and generalized skew derivations in prime rings, have been generalized to the case of [math]derivations and generalized [math]derivations.
Citation: Journal of Algebra and Its Applications
PubDate: 20211030T07:00:00Z
DOI: 10.1142/S0219498823500378

 Additive properties for the pseudo core inverse of morphisms in an
additive category
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Authors: Jianlong Chen, Xiaofeng Chen, Dingguo Wang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, given a morhism [math] with its pseudo core inverse and a morphism [math] such that is invertible, a necessary and sufficient condition and two sufficient conditions are presented under which the additive property, namely holds. Several interesting results about additive properties of core inverses of bounded linear operators presented in Huang et al. are generalized to the case of pseudo core inverse of morphism. Also, many results regarding additive properties of coreEP inverses of complex matrices studied by Ma and Stanimirović are extended to the cases of morphism.
Citation: Journal of Algebra and Its Applications
PubDate: 20211027T07:00:00Z
DOI: 10.1142/S0219498823500305

 Diamond distances in Nottingham algebras

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Authors: M. Avitabile, S. Mattarei
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Nottingham algebras are a class of justinfinitedimensional, modular, [math]graded Lie algebras, which includes the graded Lie algebra associated to the Nottingham group with respect to its lower central series. Homogeneous components of a Nottingham algebra have dimension one or two, and in the latter case they are called diamonds. The first diamond occurs in degree [math], and the second occurs in degree [math], a power of the characteristic. Many examples of Nottingham algebras are known, in which each diamond past the first can be assigned a type, either belonging to the underlying field or equal to [math]. A prospective classification of Nottingham algebras requires describing all possible diamond patterns. In this paper, we establish some crucial contributions towards that goal. One is showing that all diamonds, past the first, of an arbitrary Nottingham algebra [math] can be assigned a type, in such a way that the degrees and types of the diamonds completely describe [math]. At the same time we prove that the difference in degrees of any two consecutive diamonds in any Nottingham algebra equals [math]. As a sideproduct of our investigation, we classify the Nottingham algebras where all diamonds have type [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211027T07:00:00Z
DOI: 10.1142/S0219498823500329

 On the module of derivations of rings of invariants of [math] under the
action of certain dihedral groups
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Authors: Arindam Dey, Surjeet Kour
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we study the derivation module of the ring of invariants of [math] under the linear action of dihedral groups [math] mentioned in a paper by Riemenschneider [Die Invarianten der endlichen Untergruppen von [math], Math. Zeitsch. 153 (1977) 37–50]. We obtained an explicit generating set for the derivation module of [math]. We show that [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211027T07:00:00Z
DOI: 10.1142/S0219498823500330

 New model structures and projective (injective) cotorsion pairs

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Authors: Aimin Xu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be either the category of [math]modules or the category of chain complexes of [math]modules and [math] a cofibrantly generated hereditary abelian model structure on [math]. First, we get a new cofibrantly generated model structure on [math] related to [math] for any positive integer [math], and hence, one can get new algebraic triangulated categories. Second, it is shown that any [math]strongly Gorenstein projective module gives rise to a projective cotorsion pair cogenerated by a set. Finally, let [math] be an [math]module with finite flat dimension and [math] a positive integer, if [math] is an exact sequence of [math]modules with every [math] Gorenstein injective, then [math] is injective.
Citation: Journal of Algebra and Its Applications
PubDate: 20211027T07:00:00Z
DOI: 10.1142/S0219498823500366

 The [math] super Heisenberg–Virasoro vertex algebra at level zero

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Authors: Dražen Adamović, Berislav Jandrić, Gordan Radobolja
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We study the representation theory of the [math] super Heisenberg–Virasoro vertex algebra at level zero, which extends the previous work on the Heisenberg–Virasoro vertex algebra [D. Adamović and G. Radobolja, Free field realization of the twisted Heisenberg–Virasoro algebra at level zero and its applications, J. Pure Appl. Algebra 219(10) (2015) 4322–4342; D. Adamović and G. Radobolja, Selfdual and logarithmic representations of the twisted Heisenberg–Virasoro algebra at level zero, Commun. Contemp. Math. 21(2) (2019) 1850008; Y. Billig, Representations of the twisted Heisenberg–Virasoro algebra at level zero, Can. Math. Bull. 46(4) (2003) 529–537] to the super case. We calculated all characters of irreducible highest weight representations by investigating certain Fock space representations. Quite surprisingly, we found that the maximal submodules of certain Verma modules are generated by subsingular vectors. The formulas for singular and subsingular vectors are obtained using screening operators appearing in a study of certain logarithmic vertex algebras [D. Adamović and A. Milas, On Walgebras associated to [math] minimal models and their representations, Int. Math. Res. Notices 2010(20) (2010) 3896–3934].
Citation: Journal of Algebra and Its Applications
PubDate: 20211025T07:00:00Z
DOI: 10.1142/S0219498823500032

 Rings with [math] or [math] nilpotent

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Authors: Adel N. Abyzov, Peter V. Danchev, Daniel T. Tapkin
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a ring and let [math] be an arbitrary but fixed positive integer. We characterize those rings [math] whose elements [math] satisfy at least one of the relations that [math] or [math] is a nilpotent whenever [math]. This extends results from the same branch obtained by Danchev [A characterization of weakly J(n)rings, J. Math. Appl. 41 (2018) 53–61], Koşan et al. [Rings with [math] nilpotent, J. Algebra Appl. 19 (2020)] and Abyzov and Tapkin [On rings with [math] nilpotent, J. Algebra Appl. 21 (2022)], respectively.
Citation: Journal of Algebra and Its Applications
PubDate: 20211025T07:00:00Z
DOI: 10.1142/S021949882350024X

 Noncatastrophic convolutional codes over a finite ring

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Authors: Diego Napp, Raquel Pinto, Conceição Rocha
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Noncatastrophic encoders are an important class of polynomial generator matrices of convolutional codes. When these polynomials have coefficients in a finite field, these encoders have been characterized as polynomial left prime matrices. In this paper, we study the notion of noncatastrophicity in the context of convolutional codes when the polynomial matrices have entries in the finite ring [math]. In particular, we study the notion of zero left prime in order to fully characterize noncatastrophic encoders over the finite ring [math]. The second part of the paper is devoted to investigate free and column distance of convolutional codes that are free finitely generated [math]modules. We introduce the notion of [math]degree and provide new bounds on the free distances and column distance. We show that this class of convolutional codes is optimal with respect to the column distance and to the free distance if and only if its projection on [math] is.
Citation: Journal of Algebra and Its Applications
PubDate: 20211022T07:00:00Z
DOI: 10.1142/S0219498823500299

 Local dimension of trivial extension and amalgamation of rings

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Authors: Rachida El Khalfaoui, Najib Mahdou, Siamak Yassemi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Local dimension is an ordinal valued invariant that is in some sense a measure of how far a ring is from being local and denoted [math]. The purpose of this paper is to study the local dimension of ring extensions such as homomorphic image, trivial ring extension and the amalgamation of rings.
Citation: Journal of Algebra and Its Applications
PubDate: 20211020T07:00:00Z
DOI: 10.1142/S0219498823500238

 Characters and quantum reduction for orthosymplectic Lie superalgebras

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Authors: Namhee Kwon
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this study, we study principal admissible representations for the affine Lie superalgebra [math]. Using the character formula of irreducible admissible representations of [math], we calculate a character formula of [math]modules which are obtained from the quantized Drinfeld–Sokolov reduction and principal admissible representations. As a byproduct, we obtain the minimal series modules of the Neveu–Schwarz algebra through the [math]modules arising from the principal admissible modules over [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211020T07:00:00Z
DOI: 10.1142/S0219498823500251

 On reduced rings with prime factors simple

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Authors: PjekHwee Lee, Edmund R. Puczyłowski
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We obtain a common generalization of the results by Wong and BirkenmeierKimPark, respectively, which say that a reduced ring with unity is strongly (respectively, weakly) regular if and only if all of its prime homomorphic images are division rings (respectively, simple domains). Our arguments are different from those in the known proofs and are quite simple. They also give a characterization of weakly regular reduced rings without unity. This characterization implies in particular that the class of weakly regular reduced rings forms a radical class. However, even if a weakly regular reduced ring has no unity, its prime homomorphic images must be simple domains with unity. In the second part of the paper, we study reduced rings whose prime homomorphic images are simple domains (not necessarily with unity).
Citation: Journal of Algebra and Its Applications
PubDate: 20211020T07:00:00Z
DOI: 10.1142/S0219498823500287

 The existence of [math]Auslander–Reiten sequences via determined
morphisms
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Authors: Zongyang Xie, Zhongkui Liu, Xiaoyan Yang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative artinian ring and [math] a small Extfinite Krull–Schmidt [math]abelian [math]category with enough projectives and injectives. We introduce two full subcategories [math] and [math] of [math] in terms of the representable functors from the stable category of [math] to category of finitely generated [math]modules. Moreover, we define two additive functors [math] and [math], which are mutually quasiinverse equivalences between the stable categories of this two full subcategories. We give an equivalent characterization on the existence of [math]Auslander–Reiten sequences using determined morphisms.
Citation: Journal of Algebra and Its Applications
PubDate: 20211020T07:00:00Z
DOI: 10.1142/S0219498823500317

 Ideal structure of rings of analytic functions with nonArchimedean
metrics
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Authors: Nicholas Bruno
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The work of Helmer [Divisibility properties of integral functions, Duke Math. J. 6(2) (1940) 345–356] applied algebraic methods to the field of complex analysis when he proved the ring of entire functions on the complex plane is a Bezout domain (i.e. all finitely generated ideals are principal). This inspired the work of Henriksen [On the ideal structure of the ring of entire functions, Pacific J. Math. 2(2) (1952) 179–184. On the prime ideals of the ring of entire functions, Pacific J. Math. 3(4) (1953) 711–720] who proved a correspondence between the maximal ideals within the ring of entire functions and ultrafilters on sets of zeroes as well as a correspondence between the prime ideals and growth rates on the multiplicities of zeroes. We prove analogous results on rings of analytic functions in the nonArchimedean context: all finitely generated ideals in the ring of analytic functions on an annulus of a characteristic zero nonArchimedean field are twogenerated but not guaranteed to be principal. We also prove the maximal and prime ideal structure in the nonArchimedean context is similar to that of the ordinary complex numbers; however, the methodology has to be significantly altered to account for the failure of Weierstrass factorization on balls of finite radius in fields which are not spherically complete, which was proven by Lazard [Les zeros d’une function analytique d’une variable sur un corps value complet, Publ. Math. l’IHES 14(1) (1942) 47–75].
Citation: Journal of Algebra and Its Applications
PubDate: 20211014T07:00:00Z
DOI: 10.1142/S0219498823500111

 Model structures, recollements and duality pairs

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Authors: Wenjing Chen, Zhongkui Liu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we construct some model structures corresponding Gorenstein [math]modules and relative Gorenstein flat modules associated to duality pairs, Frobenius pairs and cotorsion pairs. By investigating homological properties of Gorenstein [math]modules and some known complete hereditary cotorsion pairs, we describe several types of complexes and obtain some characterizations of Iwanaga–Gorenstein rings. Based on some facts given in this paper, we find new duality pairs and show that [math] is covering as well as enveloping and [math] is preenveloping under certain conditions, where [math] denotes the class of Gorenstein [math]injective modules and [math] denotes the class of Gorenstein [math]flat modules. We give some recollements via projective cotorsion pair [math] cogenerated by a set, where [math] denotes the class of Gorenstein [math]projective modules. Also, many recollements are immediately displayed through setting specific complete duality pairs.
Citation: Journal of Algebra and Its Applications
PubDate: 20211014T07:00:00Z
DOI: 10.1142/S0219498823500172

 Upper bounds for the regularity of symbolic powers of certain classes of
edge ideals
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Authors: Arvind Kumar, S. Selvaraja
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a finite simple graph and [math] denote the corresponding edge ideal in a polynomial ring over a field [math]. In this paper, we obtain upper bounds for the Castelnuovo–Mumford regularity of symbolic powers of certain classes of edge ideals. We also prove that for several classes of graphs, the regularity of symbolic powers of their edge ideals coincides with that of their ordinary powers.
Citation: Journal of Algebra and Its Applications
PubDate: 20211013T07:00:00Z
DOI: 10.1142/S0219498823500160

 Distance Laplacian spectra of various graph operations and its application
to graphs on algebraic structures
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Authors: Subarsha Banerjee
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we determine the distance Laplacian spectra of graphs obtained by various graph operations. We obtain the distance Laplacian spectrum of the join of two graphs [math] and [math] in terms of adjacency spectra of [math] and [math]. Then we obtain the distance Laplacian spectrum of the join of two graphs in which one of the graphs is the union of two regular graphs. Finally, we obtain the distance Laplacian spectrum of the generalized join of graphs [math], where [math], in terms of their adjacency spectra. As applications of the results obtained, we have determined the distance Laplacian spectra of some wellknown classes of graphs, namely the zero divisor graph of [math], the commuting and the noncommuting graph of certain finite groups like [math] and [math], and the power graph of various finite groups like [math], [math] and [math]. We show that the zero divisor graph and the power graph of [math] are distance Laplacian integral for some specific [math]. Moreover, we show that the commuting and the noncommuting graph of [math] and [math] are distance Laplacian integral for all [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211009T07:00:00Z
DOI: 10.1142/S0219498823500226

 On rings whose quasiinjective modules are injective or semisimple

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Authors: Bülent Saraç
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Two obvious classes of quasiinjective modules are those of semisimples and injectives. In this paper, we study rings with no quasiinjective modules other than semisimples and injectives. We prove that such rings fall into three classes of rings, namely, (i) QIrings, (ii) rings with no middle class, or (iii) rings that decompose into a direct product of a semisimple Artinian ring and a strongly prime ring. Thus, we restrict our attention to only strongly prime rings and consider hereditary Noetherian prime rings to shed some light on this mysterious case. In particular, we prove that among these rings, QISrings which are not of type (i) or (ii) above are precisely those hereditary Noetherian prime rings which are idealizer rings from nonsimple QIoverrings.
Citation: Journal of Algebra and Its Applications
PubDate: 20211008T07:00:00Z
DOI: 10.1142/S0219498823500056

 Quasihomeomorphisms and Skula spaces

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Authors: Othman Echi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a topological space. By the Skula topology (or the [math]topology) on [math], we mean the topology [math] on [math] with basis the collection of all [math]locally closed sets of [math], the resulting space [math] will be denoted by [math]. We show that the following results hold: (1)[math] is an Alexandroff space if and only if the [math]reflection [math] of [math] is a [math]space. (2)[math] is a Noetherian space if and only if [math] is finite. (3)If we denote by [math] the Alexandroff extension of [math], then [math] if and only if [math] is a Noetherian quasisober space. We also give an alternative proof of a result due to Simmons concerning the iterated Skula spaces, namely, [math]. A space is said to be clopen if its open sets are also closed. In [R. E. Hoffmann, Irreducible filters and sober spaces, Manuscripta Math. 22 (1977) 365–380], Hoffmann introduced a refinement clopen topology [math] of [math]: The indiscrete components of [math] are of the form [math], where [math] and [math] is the intersection of all open sets of [math] containing [math] (equivalently, [math]). We show that [math]
Citation: Journal of Algebra and Its Applications
PubDate: 20211008T07:00:00Z
DOI: 10.1142/S0219498823500202

 Unit group structure of the quotient ring of a quadratic ring

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Authors: Yangjiang Wei, Huadong Su, Linhua Liang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be the rational filed. For a squarefree integer [math] with [math], we denote by [math] the quadratic field. Let [math] be the ring of algebraic integers of [math]. In this paper, we completely determine the unit group of the quotient ring [math] of [math] for an arbitrary prime [math] in [math], where [math] has the unique factorization property, and [math] is a rational integer.
Citation: Journal of Algebra and Its Applications
PubDate: 20211006T07:00:00Z
DOI: 10.1142/S021949882350010X

 Symmetric polynomials in the variety generated by Grassmann algebras

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Authors: Nazan Akdoğan, Şehmus Fındık
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] denote the variety generated by infinitedimensional Grassmann algebras, i.e. the collection of all unitary associative algebras satisfying the identity [math], where [math]. Consider the free algebra [math] in [math] generated by [math]. We call a polynomial [math] symmetric if it is preserved under the action of the symmetric group [math] on generators, i.e. [math] for each permutation [math]. The set of symmetric polynomials forms the subalgebra [math] of invariants of the group [math] in [math]. The commutator ideal [math] of the algebra [math] has a natural left [math]module structure, and [math] is a left [math]module. We give a finite free generating set for the [math]module [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211006T07:00:00Z
DOI: 10.1142/S0219498823500196

 Bivariate systems of polynomial equations with roots of high multiplicity

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Authors: I. Nikitin
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Given a bivariate system of polynomial equations with fixed support sets [math] it is natural to ask which multiplicities its solutions can have. We prove that there exists a system with a solution of multiplicity [math] for all [math] in the range [math], where [math] is the set of all integral vectors that shift B to a subset of [math]. As an application, we classify all pairs [math] such that the system supported at [math] does not have a solution of multiplicity higher than [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20211005T07:00:00Z
DOI: 10.1142/S0219498823500147

 On orthodox [math]restriction semigroups

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Authors: Shoufeng Wang, K. P. Shum
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The investigation of orthodox [math]restriction semigroups was initiated by Jones in 2014 as generalizations of orthodox [math]semigroups. The aim of this paper is to further study orthodox [math]restriction semigroups based on the known results of Jones. After establishing a construction theorem for orthodox [math]restriction semigroups, we introduce proper [math]restriction semigroups (which are necessarily orthodox) and prove that every (finite) orthodox [math]restriction semigroup has a (finite) proper cover. Our results enrich and extend existing results for restriction semigroups and orthodox [math]semigroups.
Citation: Journal of Algebra and Its Applications
PubDate: 20211005T07:00:00Z
DOI: 10.1142/S0219498823500184

 Comaximal graph of amalgamated algebras along an ideal

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Authors: Hanieh Shoar, Maryam Salimi, Abolfazl Tehranian, Hamid Rasouli, Elham Tavasoli
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] and [math] be commutative rings with identity, [math] be an ideal of [math], and let [math] be a ring homomorphism. The amalgamation of [math] with [math] along [math] with respect to [math] denoted by [math] was introduced by D’Anna et al. in 2010. In this paper, we investigate some properties of the comaximal graph of [math] which are transferred to the comaximal graph of [math], and also we study some algebraic properties of the ring [math] by way of graph theory. The comaximal graph of [math], [math], was introduced by Sharma and Bhatwadekar in 1995. The vertices of [math] are all elements of [math] and two distinct vertices [math] and [math] are adjacent if and only if [math]. Let [math] be the subgraph of [math] generated by nonunit elements, and let [math] be the Jacobson radical of [math]. It is shown that the diameter of the graph [math] is equal to the diameter of the graph [math], and the girth of the graph [math] is equal to the girth of the graph [math], provided some special conditions.
Citation: Journal of Algebra and Its Applications
PubDate: 20211005T07:00:00Z
DOI: 10.1142/S0219498823500214

 The algebraic classification of nilpotent algebras

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Authors: Ivan Kaygorodov, Mykola Khrypchenko, Samuel A. Lopes
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We give the complete algebraic classification of all complex 4dimensional nilpotent algebras. The final list has 234 (parametric families of) isomorphism classes of algebras, 66 of which are new in the literature.
Citation: Journal of Algebra and Its Applications
PubDate: 20210930T07:00:00Z
DOI: 10.1142/S0219498823500093

 On relative counterpart of Auslander’s conditions

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Authors: Driss Bennis, Rachid El Maaouy, J. R. García Rozas, Luis Oyonarte
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
It is now well known that the conditions used by Auslander to define the Gorenstein projective modules on Noetherian rings are independent. Recently, Ringel and Zhang adopted a new approach in investigating Auslander’s conditions. Instead of looking for examples, they investigated rings on which certain implications between Auslander’s conditions hold. In this paper, we investigate the relative counterpart of Auslander’s conditions. So, we extend Ringel and Zhang’s work and introduce other concepts. Namely, for a semidualizing module [math], we introduce weakly [math]Gorenstein and partially [math]Gorenstein rings as rings representing relations between the relative counterpart of Auslander’s conditions. Moreover, we introduce a relative notion of the wellknown Frobenius category. We show how useful are [math]Frobenius categories in characterizing weakly [math]Gorenstein and partially [math]Gorenstein rings.
Citation: Journal of Algebra and Its Applications
PubDate: 20210930T07:00:00Z
DOI: 10.1142/S0219498823500159

 Hopf algebras on planar trees and permutations

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Authors: Diego Arcis, Sebastián Márquez
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We endow the space of rooted planar trees with the structure of a Hopf algebra. We prove that variations of such a structure lead to Hopf algebras on the spaces of labeled trees, [math]trees, increasing planar trees and sorted trees. These structures are used to construct Hopf algebras on different types of permutations. In particular, we obtain new characterizations of the Hopf algebras of Malvenuto–Reutenauer and Loday–Ronco via planar rooted trees.
Citation: Journal of Algebra and Its Applications
PubDate: 20210929T07:00:00Z
DOI: 10.1142/S0219498822502243

 CInjective rings

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Authors: Liang Shen, Feng Feng, Wenxi Li
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
A ring [math] is called a right Cinjective ring if every homomorphism from a closed right ideal of [math] to [math] can be extended to one from [math] to [math]. It is clear that a right CS ring must be right Cinjective. Left Cinjective rings can be defined similarly. Properties of Cinjective rings are explored in this paper. It is shown that a left Cinjective ring may not be right Cinjective and a right Cinjective ring may not be right CS. Some extensions of Cinjective rings are discussed.
Citation: Journal of Algebra and Its Applications
PubDate: 20210929T07:00:00Z
DOI: 10.1142/S0219498822502371

 Ring of flows of onedimensional differential equations

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Authors: Ronald Orozco
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we construct a ring of flows, where we can decompose onedimensional autonomous differential equations into smaller parts, then solve each part and finally put everything together to obtain the exact solution of these equations.
Citation: Journal of Algebra and Its Applications
PubDate: 20210929T07:00:00Z
DOI: 10.1142/S0219498823500044

 Filtrations on block subalgebras of reduced enveloping algebras

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Authors: Andrei Ionov, Dylan Pentland
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We study the interaction between the block decompositions of reduced enveloping algebras in positive characteristic, the PoincaréBirkhoffWitt (PBW) filtration, and the nilpotent cone. We provide two natural versions of the PBW filtration on the block subalgebra [math] of the restricted universal enveloping algebra [math] and show these are dual to each other. We also consider a shifted PBW filtration for which we relate the associated graded algebra to the algebra of functions on the Frobenius neighborhood of [math] in the nilpotent cone and the coinvariants algebra corresponding to [math]. In the case of [math] in characteristic [math] we determine the associated graded algebras of these filtrations on block subalgebras of [math]. We also apply this to determine the structure of the adjoint representation of [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210924T07:00:00Z
DOI: 10.1142/S0219498823500019

 Braided Frobenius algebras from certain Hopf algebras

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Authors: Masahico Saito, Emanuele Zappala
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
A braided Frobenius algebra is a Frobenius algebra with a Yang–Baxter operator that commutes with the operations, that are related to diagrams of compact surfaces with boundary expressed as ribbon graphs. A heap is a ternary operation exemplified by a group with the operation [math], that is ternary selfdistributive. Hopf algebras can be endowed with the algebra version of the heap operation. Using this, we construct braided Frobenius algebras from a class of certain Hopf algebras that admit integrals and cointegrals. For these Hopf algebras we show that the heap operation induces a Yang–Baxter operator on the tensor product, which satisfies the required compatibility conditions. Diagrammatic methods are employed for proving commutativity between Yang–Baxter operators and Frobenius operations.
Citation: Journal of Algebra and Its Applications
PubDate: 20210923T07:00:00Z
DOI: 10.1142/S0219498823500123

 On [math]symmetric polynomials

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Authors: Jing Yang, Chee K. Yap
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We study functions of the roots of an integer polynomial [math] with [math] distinct roots [math] of multiplicity [math], [math]. Traditionally, root functions are studied via the theory of symmetric polynomials; we generalize this theory to [math]symmetric polynomials. We initiate the study of the vector space of [math]symmetric polynomials of a given degree [math] via the concepts of [math]gist and [math]ideal. In particular, we are interested in the root function [math]. The Dplus discriminant of [math] is [math]. This quantity appears in the complexity analysis of the root clustering algorithm of Becker et al. (ISSAC 2016). We conjecture that [math] is [math]symmetric, which implies [math] is rational. To explore this conjecture experimentally, we introduce algorithms for checking if a given root function is [math]symmetric. We design three such algorithms: one based on Gröbner bases, another based on canonical bases and reduction, and the third based on solving linear equations. Each of these algorithms has variants that depend on the choice of a basis for the [math]symmetric functions. We implement these algorithms (and their variants) in Maple and experiments show that the latter two algorithms are significantly faster than the first.
Citation: Journal of Algebra and Its Applications
PubDate: 20210915T07:00:00Z
DOI: 10.1142/S0219498822502334

 Homotopy liftings and Hochschild cohomology of some twisted tensor
products
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Authors: Pablo S. Ocal, Tolulope Oke, Sarah Witherspoon
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The Hochschild cohomology of a tensor product of algebras is isomorphic to a graded tensor product of Hochschild cohomology algebras, as a Gerstenhaber algebra. A similar result holds when the tensor product is twisted by a bicharacter. We present new proofs of these isomorphisms, using Volkov’s homotopy liftings that were introduced for handling Gerstenhaber brackets expressed on arbitrary bimodule resolutions. Our results illustrate the utility of homotopy liftings for theoretical purposes.
Citation: Journal of Algebra and Its Applications
PubDate: 20210911T07:00:00Z
DOI: 10.1142/S0219498822502383

 Congruences on glrac semigroups (I)

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Authors: Haijun Liu, Xiaojiang Guo
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The theory of congruences on semigroups is an important part in the theory of semigroups. The aim of this paper is to study [math]congruences on a glrac semigroup. It is proved that the [math]congruences on a glrac semigroup become a complete sublattice of its lattice of congruences. Especially, the structures of left restriction semigroup [math]congruences and the projectionseparating [math]congruences on a glrac semigroup are established. Also, we demonstrate that they are both complete sublattice of [math]congruences and consider their relations with respect to complete lattice homomorphism.
Citation: Journal of Algebra and Its Applications
PubDate: 20210911T07:00:00Z
DOI: 10.1142/S0219498822502401

 Strongly [math][math]irreducible ideals

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Authors: Ahmad Yousefian Darani, Najib Mahdou, Sanae Moussaoui
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative ring, [math] be an ideal of [math], [math] be a nonnull positive integer and [math] be a function where [math] is the set of ideals of [math]. In this paper, we define a new generalization of strongly [math]irreducible ideals called strongly [math][math]irreducible ideal, that is, whenever [math] and [math] for [math] ideals of [math], then there are [math] of the [math]’s whose intersection is in [math]. We study the stability of this new concept with respect to various ringtheoretic constructions such as the trivial ring extension and the amalgamation of rings along an ideal.
Citation: Journal of Algebra and Its Applications
PubDate: 20210911T07:00:00Z
DOI: 10.1142/S0219498823500020

 Artin–Schelter regular algebras of dimension five with three
generators
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Authors: Jun Li
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we investigate Artin–Schelter regular algebras of dimension [math] with three generators in degree [math] under the hypothesis that [math], in which the degree types of the relations for the number of the generating relations less than five can be determined. We prove that the only possible degree type of three generating relations is [math] and the only possible degree type of four generating relations is [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210910T07:00:00Z
DOI: 10.1142/S0219498822502358

 Ktheory of [math]coherent rings

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Authors: Eugenia Ellis, Rafael Parra
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a strong [math]coherent ring such that each finitely [math]presented [math]module has finite projective dimension. We consider [math] the full subcategory of [math]Mod of finitely [math]presented modules. We prove that [math] is an exact category, [math] for every [math] and we obtain an expression of [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210910T07:00:00Z
DOI: 10.1142/S021949882350007X

 Orthogonal decompositions of Lie algebras over finite commutative rings

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Authors: Songpon Sriwongsa
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a finite commutative ring with identity. In this paper, we give a necessary condition for the existence of an orthogonal decomposition of the special linear Lie algebra over [math]. Additionally, we study orthogonal decompositions of the symplectic Lie algebra and the special orthogonal Lie algebra over [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210908T07:00:00Z
DOI: 10.1142/S0219498823500068

 Multipliers and unicentral Leibniz algebras

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Authors: Erik Mainellis
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we prove Leibniz analogues of results found in Peggy Batten’s 1993 dissertation. We first construct a Hochschild–Serretype spectral sequence of low dimension, which is used to characterize the multiplier in terms of the second cohomology group with coefficients in the field. The sequence is then extended by a term and a Ganea sequence is constructed for Leibniz algebras. The maps involved with these exact sequences, as well as a characterization of the multiplier, are used to establish criteria for when a central ideal is contained in a certain set seen in the definition of unicentral Leibniz algebras. These criteria are then specialized, and we obtain conditions for when the center of the cover maps onto the center of the algebra.
Citation: Journal of Algebra and Its Applications
PubDate: 20210908T07:00:00Z
DOI: 10.1142/S0219498823500081

 Some variations of projectivity

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Authors: Nil Orhan Ertaş, Rachid Tribak
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We prove that a ring [math] has a module [math] whose domain of projectivity consists of only some injective modules if and only if [math] is a right noetherian right [math]ring. Also, we consider modules which are projective relative only to a subclass of max modules. Such modules are called maxpoor modules. In a recent paper Holston et al. showed that every ring has a ppoor module (that is a module whose projectivity domain consists precisely of the semisimple modules). So every ring has a maxpoor module. The structure of all maxpoor abelian groups is completely determined. Examples of rings having a maxpoor module which is neither projective nor ppoor are provided. We prove that the class of maxpoor [math]modules is closed under direct summands if and only if [math] is a right Bass ring. A ring [math] is said to have no right maxpmiddle class if every right [math]module is either projective or maxpoor. It is shown that if a commutative noetherian ring [math] has no right maxpmiddle class, then [math] is the ring direct sum of a semisimple ring [math] and a ring [math] which is either zero or an artinian ring or a onedimensional local noetherian integral domain such that the quotient field [math] of [math] has a proper [math]submodule which is not complete in its [math]topology. Then we show that a commutative noetherian hereditary ring [math] has no right maxpmiddle class if and only if [math] is a semisimple ring.
Citation: Journal of Algebra and Its Applications
PubDate: 20210904T07:00:00Z
DOI: 10.1142/S021949882250236X

 Almost split morphisms in subcategories of triangulated categories

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Authors: Francesca Fedele
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
For a suitable triangulated category [math] with a Serre functor [math] and a full precovering subcategory [math] closed under summands and extensions, an indecomposable object [math] in [math] is called Extprojective if Ext[math]. Then there is no Auslander–Reiten triangle in [math] with end term [math]. In this paper, we show that if, for such an object [math], there is a minimal right almost split morphism [math] in [math], then [math] appears in something very similar to an Auslander–Reiten triangle in [math]: an essentially unique triangle in [math] of the form Δ = X →ξB →βC → ΣX, where [math] is an indecomposable not in [math] and [math] is a [math]envelope of [math]. Moreover, under some extra assumptions, we show that removing [math] from [math] and replacing it with [math] produces a new subcategory of [math] closed under extensions. We prove that this process coincides with the classic mutation of [math] with respect to the rigid subcategory of [math] generated by all the indecomposable Extprojectives in [math] apart from [math]. When [math] is the cluster category of Dynkin type [math] and [math] has the above properties, we give a full description of the triangles in [math] of the form [math] and show under which circumstances replacing [math] by [math] gives a new extension closed subcategory.
Citation: Journal of Algebra and Its Applications
PubDate: 20210831T07:00:00Z
DOI: 10.1142/S0219498822502395

 Graded torsionfree [math]modules of rank 2

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Authors: Yuri Bahturin, Abdallah Shihadeh
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we explore the possibility of endowing simple infinitedimensional [math]modules by the structure of graded modules. The gradings on the finitedimensional simple modules over simple Lie algebras have been studied in 7, 8.
Citation: Journal of Algebra and Its Applications
PubDate: 20210828T07:00:00Z
DOI: 10.1142/S0219498822502292

 Branching rules and commuting probabilities for Triangular and
Unitriangular matrices
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Authors: Dilpreet Kaur, Uday Bhaskar Sharma, Anupam Singh
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
This paper concerns the enumeration of simultaneous conjugacy classes of [math]tuples of commuting matrices in the upper triangular group [math] and unitriangular group [math] over the finite field [math] of odd characteristic. This is done for [math] and [math], by computing the branching rules. Further, using the branching matrix thus computed, we explicitly get the commuting probabilities [math] for [math] in each case.
Citation: Journal of Algebra and Its Applications
PubDate: 20210828T07:00:00Z
DOI: 10.1142/S0219498822502310

 On some estimates and topological properties of relative orbits of subsets

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Authors: Dao Phuong Bac
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we give some topological properties and estimates of orbit of certain subsets of [math]points of varieties under actions of algebraic tori. These results are concerned with an analogue of BruhatTits’ question on the set of [math]adic integral points of algebraic tori.
Citation: Journal of Algebra and Its Applications
PubDate: 20210828T07:00:00Z
DOI: 10.1142/S0219498822502413

 RLWE/PLWE equivalence for totally real cyclotomic subextensions via
quasiVandermonde matrices
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Authors: Iván BlancoChacón
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We propose and justify a generalized approach to prove the polynomial reduction of the RLWE to the PLWE problem attached to the ring of integers of a monogenic number field. We prove such equivalence in the case of the maximal totally real subextension of the [math]th cyclotomic field, with [math] arbitrary prime.
Citation: Journal of Algebra and Its Applications
PubDate: 20210819T07:00:00Z
DOI: 10.1142/S0219498822502188

 Paramedial quasigroups of prime and prime square order

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Authors: Žaneta Semanišinová
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We prove that, for every odd prime number [math], there are [math] paramedial quasigroups of order [math] and [math] paramedial quasigroups of order [math], up to isomorphism. We present a complete list of those which are simple.
Citation: Journal of Algebra and Its Applications
PubDate: 20210819T07:00:00Z
DOI: 10.1142/S0219498822502346

 Quaternion rings over local rings

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Authors: Isao Kikumasa, Kiyoichi Oshiro
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In 1843, Hamilton (1805–1865) discovered the 4dimensional division algebra [math] over the field [math] of real numbers. Hamilton’s big discovery is the following beautiful multiplications for the basis [math]: (*) i2 = j2 = k2 = ijk = −1. [math] contains the field [math] of complex numbers; therefore [math]. Frobenius (1849–1917) showed the following outstanding theorem. Theorem (Frobenius). Up to isomorphism, the only finitedimensional noncommutative division algebra over [math] is [math]. Starting from given any ring [math] and a free right [math]module [math], the quaternion ring [math] is canonically defined by the multiplications [math]. For a commutative field [math] with [math], [math] is a division ring or isomorphic to the ring of [math] matrices over [math]. This is a classical theorem. For nonzero [math] in the center of a ring [math], the generalized quaternion ring [math] is defined. [math] is [math]. In [I. Kikumasa, K. Koike and K. Oshiro, Complex rings and quaternion rings, EastWest J. Math. 21 (2019) 1–19; I. Kikumasa, G. Lee and K. Oshiro, Complex Rings, Quaternion Rings and Octonion Rings (Lambert Academic Publishing, 2020); G. Lee and K. Oshiro, Quaternion rings and octonion rings, Front. Math. China 12(1) (2017) 143–155], quaternion rings and generalized quaternion rings over division rings or other rings are studied. Now, in this paper, from ring theoretic viewpoints, we study quaternion rings [math] and generalized quaternion rings [math] over local rings [math]. From our results, we can clearly look over several classical results on [math] and [math] over commutative fields [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210817T07:00:00Z
DOI: 10.1142/S021949882250219X

 On the supersolvability of a finite group by the sum of subgroup orders

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Authors: Marius Tărnăuceanu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a finite group and [math]. In this paper, we prove that if [math], then [math] is supersolvable. In particular, some new characterizations of the wellknown groups [math] and [math] are obtained. We also show that [math] does not imply the supersolvability of [math] for no constant [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210817T07:00:00Z
DOI: 10.1142/S0219498822502322

 A class of Lie racks associated to symmetric Leibniz algebras

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Authors: Hamid Abchir, Fatimaezzahrae Abid, Mohamed Boucetta
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We classify symmetric Leibniz algebras in dimensions 3 and 4 and we determine all associated Lie racks. Some of such Lie racks give rise to nontrivial topological quandles. We study some algebraic properties of these quandles and we give a necessary and sufficient condition for them to be quasitrivial.
Citation: Journal of Algebra and Its Applications
PubDate: 20210816T07:00:00Z
DOI: 10.1142/S0219498822502309

 Linear permutations and their compositional inverses over [math]

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Authors: Gustavo Terra Bastos
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The use of permutation polynomials over finite fields has appeared, along with their compositional inverses, as a good choice in the implementation of cryptographic systems. As a particular case, the construction of involutions is highly desired since their compositional inverses are themselves. In this work, we present an effective way of how to construct several linear permutation polynomials over [math] as well as their compositional inverses using a decomposition of [math] based on its primitive idempotents. As a consequence, involutions are also constructed.
Citation: Journal of Algebra and Its Applications
PubDate: 20210813T07:00:00Z
DOI: 10.1142/S0219498822502206

 On [math]generalized commutators and Lie ideals of rings

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Authors: Peter V. Danchev, TsiuKwen Lee
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an associative ring. Given a positive integer [math], for [math] we define [math], the [math]generalized commutator of [math]. By an [math]generalized Lie ideal of [math] (at the [math]th position with [math]) we mean an additive subgroup [math] of [math] satisfying [math] for all [math] and all [math], where [math]. In the paper, we study [math]generalized commutators of rings and prove that if [math] is a noncommutative prime ring and [math], then every nonzero [math]generalized Lie ideal of [math] contains a nonzero ideal. Therefore, if [math] is a noncommutative simple ring, then [math]. This extends a classical result due to Herstein [Generalized commutators in rings, Portugal. Math. 13 (1954) 137–139]. Some generalizations and related questions on [math]generalized commutators and their relationship with noncommutative polynomials are also discussed.
Citation: Journal of Algebra and Its Applications
PubDate: 20210813T07:00:00Z
DOI: 10.1142/S0219498822502218

 Galois extensions for quasigroupoid magmas

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Authors: R. González Rodríguez
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we extend the result proved by Ulbrich about the characterization of Galois extensions linked to group algebras upon the nonassociative (quasigroup) quasigroupoid magma setting. Also, as a particular instance of the results contained in this paper, we obtain the ones proved for Galois extensions related with groupoid algebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20210813T07:00:00Z
DOI: 10.1142/S0219498822502231

 Pairs of domains where all intermediate domains satisfy [math]ACCP

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Authors: S. Visweswaran
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The rings considered in this paper are commutative with identity. If [math] is a subring of a ring [math], then we assume that [math] contains the identity element of [math]. Let [math] be a multiplicatively closed subset (m.c. subset) of a ring [math]. An increasing sequence of ideals [math] of [math] is said to be [math]stationary if there exist [math] and [math] such that [math] for all [math]. This paper is motivated by the research work [A. Hamed and H. Kim, On integral domains in which every ascending chain on principal ideals is [math]stationary, Bull. Korean Math. Soc. 57(5) (2020) 1215–1229]. Let [math] be a m.c. subset of an integral domain [math]. We say that [math] satisfies [math]ACCP if every increasing sequence of principal ideals of [math] is [math]stationary. Let [math] be a subring of an integral domain [math] and let [math] be a m.c. subset of [math]. We say that [math] is an [math]ACCP pair if [math] satisfies [math]ACCP for every subring [math] of [math] with [math]. The aim of this paper is to provide some pairs of domains [math] such that [math] is an [math]ACCP pair, where [math] is a m.c. subset of [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210813T07:00:00Z
DOI: 10.1142/S0219498822502280

 Antiflexible bialgebras

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Authors: Mafoya Landry Dassoundo, Chengming Bai, Mahouton Norbert Hounkonnou
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We establish a bialgebra theory for antiflexible algebras in this paper. We introduce the notion of an antiflexible bialgebra which is equivalent to a Manin triple of antiflexible algebras. The study of a special case of antiflexible bialgebras leads to the introduction of antiflexible Yang–Baxter equation in an antiflexible algebra which is an analogue of the classical Yang–Baxter equation in a Lie algebra or the associative Yang–Baxter equation in an associative algebra. It is unexpected consequence that both the antiflexible Yang–Baxter equation and the associative Yang–Baxter equation have the same form. A skewsymmetric solution of antiflexible Yang–Baxter equation gives an antiflexible bialgebra. Finally the notions of an [math]operator of an antiflexible algebra and a preantiflexible algebra are introduced to construct skewsymmetric solutions of antiflexible Yang–Baxter equation.
Citation: Journal of Algebra and Its Applications
PubDate: 20210804T07:00:00Z
DOI: 10.1142/S0219498822502127

 Prime and semiprime submodules of [math] and a related Nullstellensatz for
[math]
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Authors: J. Cimprič
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative ring with [math] and [math] a natural number. We say that a submodule [math] of [math] is semiprime if for every [math] such that [math] for [math] we have [math]. Our main result is that every semiprime submodule of [math] is equal to the intersection of all prime submodules containing it. It follows that every semiprime left ideal of [math] is equal to the intersection of all prime left ideals that contain it. For [math] where [math] is an algebraically closed field we can rephrase this result as a Nullstellensatz for [math]: For every [math], [math] belongs to the smallest semiprime left ideal of [math] that contains [math] iff for every [math] and [math] such that [math] we have [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210804T07:00:00Z
DOI: 10.1142/S0219498822502176

 A note on the regular ideals of Leavitt path algebras

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Authors: Daniel Gonçalves, Danilo Royer
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We show that, for an arbitrary graph, a regular ideal of the associated Leavitt path algebra is also graded. As a consequence, for a rowfinite graph, we obtain that the quotient of the associated Leavitt path by a regular ideal is again a Leavitt path algebra and that Condition (L) is preserved by quotients by regular ideals. Furthermore, we describe the vertex set of a regular ideal and make a comparison between the theory of regular ideals in Leavitt path algebras and in graph C*algebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20210804T07:00:00Z
DOI: 10.1142/S0219498822502255

 On characterization of a finite group by the set of conjugacy class sizes

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Authors: Ilya Gorshkov
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a finite group and [math] be the set of its conjugacy class sizes. In the 1980s, Thompson conjectured that the equality [math], where [math] and [math] is simple, implies the isomorphism [math]. In a series of papers of different authors, Thompson’s conjecture was proved. In this paper, we show that in some cases it is possible to omit the conditions [math] and [math] is simple and prove a more general result.
Citation: Journal of Algebra and Its Applications
PubDate: 20210804T07:00:00Z
DOI: 10.1142/S0219498822502267

 Extensions of several coprime results to good action case

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Authors: Gülı̇n Ercan, İsmaı̇l Ş. Güloğlu, Enrico Jabara
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] and [math] be groups where [math] acts on [math] by automorphisms. We say “the action of[math] on[math] is good” if the equality [math] holds for any subgroup [math] of [math] and for any [math]invariant subgroup [math] of [math]. It is straightforward that every coprime action is a good action. In this work, we extend some results due to Ward, Gross, Shumyatsky, Jabara and Meng and Guo under coprime action to good action.
Citation: Journal of Algebra and Its Applications
PubDate: 20210729T07:00:00Z
DOI: 10.1142/S021949882250222X

 Strongly Gorenstein categories

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Authors: Wan Wu, Zenghui Gao
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We introduce and study strongly Gorenstein subcategory [math], relative to an additive full subcategory [math] of an abelian category [math]. When [math] is selforthogonal, we give some sufficient conditions under which the property of an object in [math] can be inherited by its subobjects and quotient objects. Then, we introduce the notions of onesided (strongly) Gorenstein subcategories. Under the assumption that [math] is closed under countable direct sums (respectively, direct products), we prove that an object is in right (respectively, left) Gorenstein category [math] (respectively, [math]) if and only if it is a direct summand of an object in right (respectively, left) strongly Gorenstein subcategory [math] (respectively, [math]). As applications, some known results are obtained as corollaries.
Citation: Journal of Algebra and Its Applications
PubDate: 20210724T07:00:00Z
DOI: 10.1142/S0219498822502139

 Generating infinite monoids of cellular automata

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Authors: Alonso CastilloRamirez
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
For a group [math] and a set [math], let [math] be the monoid of all cellular automata over [math], and let [math] be its group of units. By establishing a characterization of surjunctive groups in terms of the monoid [math], we prove that the rank of [math] (i.e. the smallest cardinality of a generating set) is equal to the rank of [math] plus the relative rank of [math] in [math], and that the latter is infinite when [math] has an infinite decreasing chain of normal subgroups of finite index, condition which is satisfied, for example, for any infinite residually finite group. Moreover, when [math] is a vector space over a field [math], we study the monoid [math] of all linear cellular automata over [math] and its group of units [math]. We show that if [math] is an indicable group and [math] is finitedimensional, then [math] is not finitely generated; however, for any finitely generated indicable group [math], the group [math] is finitely generated if and only if [math] is finite.
Citation: Journal of Algebra and Its Applications
PubDate: 20210724T07:00:00Z
DOI: 10.1142/S0219498822502152

 Lcmlattice, Taylor bases and minimal free resolutions of a monomial ideal

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Authors: RiXiang Chen
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We give a new method to construct minimal free resolutions of all monomial ideals. This method relies on two concepts: one is the wellknown lcmlattice of a monomial ideal; the other is a new concept called Taylor basis, which describes how a minimal free resolution can be embedded in Taylor resolution. An approximation formula for minimal free resolutions of all monomial ideals is also obtained.
Citation: Journal of Algebra and Its Applications
PubDate: 20210724T07:00:00Z
DOI: 10.1142/S0219498822502164

 The existence of left eigenvalues for quaternionic matrix

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Authors: Yan Yang, Kit Ian Kou
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this work, an algebraic method to prove the existence of left eigenvalues for the quaternionic matrix is investigated. The left eigenvalues of a [math] quaternionic matrix can be derived by solving the zeros of a general quaternionic polynomial of degree [math]. Using the Study’s determinant, it can be found by solving the zeros of quaternionic polynomials of degree at most [math] or of rational functions.
Citation: Journal of Algebra and Its Applications
PubDate: 20210722T07:00:00Z
DOI: 10.1142/S0219498822502073

 Note on strongly quasiprimary ideals

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Authors: Ibtesam Alshammari, Rania Kammoun, Abdellah Mamouni, Mohammed Tamekkante
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative ring with [math]. A proper ideal [math] of [math] is said to be a strongly quasiprimary ideal if, whenever [math] with [math], then either [math] or [math]. In this paper, we characterize Noetherian and reduced rings over which every (respectively, nonzero) proper ideal is strongly quasiprimary. We also characterize ring over which every strongly quasi primary ideal of [math] is prime. Many examples are given to illustrate the obtained results.
Citation: Journal of Algebra and Its Applications
PubDate: 20210721T07:00:00Z
DOI: 10.1142/S0219498822502012

 Spectrum of the zerodivisor graph of von Neumann regular rings

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Authors: Avinash Patil, Kiran Shinde
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The zerodivisor graph [math] of a commutative ring [math] is the graph whose vertices are the nonzero zero divisors in [math] and two vertices [math] and [math] are adjacent if and only if [math]. We study the adjacency and Laplacian eigenvalues of the zerodivisor graph [math] of a finite commutative von Neumann regular ring [math]. We prove that [math] is a generalized join of its induced subgraphs. Among the [math] eigenvalues (respectively, Laplacian eigenvalues) of [math], exactly [math] are the eigenvalues of a matrix obtained from the adjacency (respectively, Laplacian) matrix of [math]the zerodivisor graph of nontrivial idempotents in [math]. We also determine the degree of each vertex in [math], hence the number of edges.
Citation: Journal of Algebra and Its Applications
PubDate: 20210715T07:00:00Z
DOI: 10.1142/S0219498822501936

 Borel subalgebras of restricted CartanType Lie algebras

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Authors: Ke Ou, Bin Shu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
It is still an open problem to determine the conjugacy classes of Borel subalgebras of nonclassical type Lie algebras. In this paper, we prove that there are at least 2 conjugacy classes of Borel subalgebras as well as maximal triangulable subalgebras of restricted Cartan type Lie algebras of type W, S and H. We are particularly interested in maximal triangulable subalgebras of [math] under some conditions which is called [math]subalgebras (Definition 3.1). We classify the conjugacy classes of [math]subalgebras for [math] and determine their representatives. This paper and its sequel [Z. Lin, K. Ou and B. Shu, Geometric Setting of Jacobson–Witt Algebras, preprint] attempt to establish both algebraic and geometric setting for geometric representation theory of [math]
Citation: Journal of Algebra and Its Applications
PubDate: 20210715T07:00:00Z
DOI: 10.1142/S0219498822502103

 Families of generalized Cohen–Macaulay and filter rings

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Authors: Y. Azimi, N. Shirmohammadi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative ring with unity, [math] and [math] an ideal of [math]. Define [math] to be [math] a quotient of the Rees algebra. In this paper, we investigate when the rings in the family are generalized Cohen–Macaulay or filter rings and show that these properties are independent of the choice of [math] and [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210715T07:00:00Z
DOI: 10.1142/S0219498822502140

 Injective and projective semimodules over involutive semirings

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Authors: Peter Jipsen, Sara Vannucci
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We show that the term equivalence between MValgebras and MVsemirings lifts to involutive residuated lattices and a class of semirings called involutive semirings. The semiring perspective leads to a necessary and sufficient condition for the interval [math] to be a subalgebra of an involutive residuated lattice, where [math] is the dualizing element. We also import some results and techniques of semimodule theory in the study of this class of semirings, generalizing results about injective and projective MVsemimodules. Indeed, we note that the involution plays a crucial role and that the results for MVsemirings are still true for involutive semirings whenever the Mundici functor is not involved. In particular, we prove that involution is a necessary and sufficient condition in order for projective and injective semimodules to coincide.
Citation: Journal of Algebra and Its Applications
PubDate: 20210709T07:00:00Z
DOI: 10.1142/S0219498822501821

 The fineness properties of Morita contexts

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Authors: Yiqiang Zhou
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a Morita context. For generalized fine (respectively, generalized unitfine) rings [math] and [math], it is proved that [math] is generalized fine (respectively, generalized unitfine) if and only if, for [math] and [math], [math] implies [math] and [math] implies [math]. Especially, for fine (respectively, unitfine) rings [math] and [math], [math] is fine (respectively, unitfine) if and only if, for [math] and [math], [math] implies [math] and [math] implies [math]. As consequences, (1) matrix rings over fine (respectively, unitfine, generalized fine and generalized unitfine) rings are fine (respectively, unitfine, generalized fine and generalized unitfine); (2) a sufficient condition for a simple ring to be fine (respectively, unitfine) is obtained: a simple ring [math] is fine (respectively, unitfine) if both [math] and [math] are fine (respectively, unitfine) for some [math]; and (3) a question of Cǎlugǎreanu [1] on unitfine matrix rings is affirmatively answered.
Citation: Journal of Algebra and Its Applications
PubDate: 20210709T07:00:00Z
DOI: 10.1142/S021949882250205X

 Annihilators of power values of derivations on Lie ideals of prime rings

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Authors: ChengKai Liu, YuanTsung Tsai
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a prime ring with the extended centroid [math] and [math] a noncentral Lie ideal of [math]. Suppose that [math], [math] and [math] is a derivation of [math] such that [math] for all [math], where [math] are fixed positive integers. If [math] or [math], then [math] unless [math], the [math] matrix ring over a field [math]. This result gives an affirmative answer to the open conjecture recently raised by Huang in [Derivations with annihilator conditions on Lie ideals in prime rings, J. Algebra Appl. 19 (2020) 2050025].
Citation: Journal of Algebra and Its Applications
PubDate: 20210706T07:00:00Z
DOI: 10.1142/S0219498822501924

 On quasi Steinberg characters of symmetric and alternating groups and
their double covers
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Authors: Digjoy Paul, Pooja Singla
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
An irreducible character of a finite group [math] is called quasi [math]Steinberg character for a prime [math] if it takes a nonzero value on every [math]regular element of [math]. In this paper, we classify the quasi [math]Steinberg characters of Symmetric ([math]) and Alternating ([math]) groups and their double covers. In particular, an existence of a nonlinear quasi [math]Steinberg character of [math] implies [math] and of [math] implies [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210706T07:00:00Z
DOI: 10.1142/S0219498822501997

 Structure and isomorphisms of quantum generalized Heisenberg algebras

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Authors: Samuel A. Lopes, Farrokh Razavinia
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In [S. A. Lopes and F. Razavinia, Quantum generalized Heisenberg algebras and their representations, preprint (2020), arXiv:2004.09301] we introduced a new class of algebras, which we named quantum generalized Heisenberg algebras and which depend on a parameter [math] and two polynomials [math]. We have shown that this class includes all generalized Heisenberg algebras (as defined in [E. M. F. Curado and M. A. RegoMonteiro, Multiparametric deformed Heisenberg algebras: A route to complexity, J. Phys. A: Math. Gen. 34(15) (2001) 3253; R. Lü and K. Zhao, Finitedimensional simple modules over generalized Heisenberg algebras, Linear Algebra Appl. 475 (2015) 276–291, MR 3325233]) as well as generalized downup algebras (as defined in [G. Benkart and T. Roby, Downup algebras, J. Algebra 209(1) (1998) 305–344; T. Cassidy and B. Shelton, Basic properties of generalized downup algebras, J. Algebra 279(1) (2004) 402–421, MR 2078408 (2005f:16051)]), but the parameters of freedom we allow for give rise to many algebras which are in neither one of these two classes. Having classified their finitedimensional irreducible representations in [S. A. Lopes and F. Razavinia, Quantum generalized Heisenberg algebras and their representations, preprint (2020), arXiv:2004.09301], in this paper, we turn to their classification by isomorphism, the description of their automorphism groups and the study of their ringtheoretical properties.
Citation: Journal of Algebra and Its Applications
PubDate: 20210706T07:00:00Z
DOI: 10.1142/S0219498822502048

 Relative global Gorenstein dimensions

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Authors: Víctor Becerril
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an abelian category. In this paper, we investigate the global [math]Gorenstein projective dimension [math], associated to a GPadmissible pair [math]. We give homological conditions over [math] that characterize it. Moreover, given a GIadmissible pair [math], we study conditions under which [math] and [math] are the same.
Citation: Journal of Algebra and Its Applications
PubDate: 20210706T07:00:00Z
DOI: 10.1142/S0219498822502085

 Leavitt path algebras for power graphs of finite groups

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Authors: Sumanta Das, M. K. Sen, S. K. Maity
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The aim of this paper is the characterization of algebraic properties of Leavitt path algebra of the directed power graph [math] and also of the directed punctured power graph [math] of a finite group [math]. We show that Leavitt path algebra of the power graph [math] of finite group [math] over a field [math] is simple if and only if [math] is a direct sum of finitely many cyclic groups of order 2. Finally, we prove that the Leavitt path algebra [math] is a prime ring if and only if [math] is either cyclic [math]group or generalized quaternion [math]group.
Citation: Journal of Algebra and Its Applications
PubDate: 20210706T07:00:00Z
DOI: 10.1142/S0219498822502097

 Some remarks on Nonnilcoherent rings and [math]IF rings

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Authors: Wei Qi, Xiaolei Zhang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative ring. If the nilpotent radical [math] of [math] is a divided prime ideal, then [math] is called a [math]ring. In this paper, we first distinguish the classes of nonnilcoherent rings and [math]coherent rings introduced by Bacem and Ali [Nonnilcoherent rings, Beitr. Algebra Geom. 57(2) (2016) 297–305], and then characterize nonnilcoherent rings in terms of [math]flat modules, nonnilinjective modules and nonnilFPinjective modules. A [math]ring [math] is called a [math]IF ring if any nonnilinjective module is [math]flat. We obtain some moduletheoretic characterizations of [math]IF rings. Two examples are given to distinguish [math]IF rings and IF [math]rings.
Citation: Journal of Algebra and Its Applications
PubDate: 20210706T07:00:00Z
DOI: 10.1142/S0219498822502115

 On the adjacency spectrum of zero divisor graph of ring [math]

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Authors: Saraswati Bajaj, Pratima Panigrahi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The zero divisor graph [math] of a commutative ring [math] with unity is a simple undirected graph whose vertices are all nonzero zero divisors of [math] and two distinct vertices [math] and [math] are adjacent if and only if [math]. In this paper, we study the graphical structure and the adjacency spectrum of the zero divisor graph of ring [math]. For any nonprime positive integer [math] with [math] number of proper divisors, we show that the adjacency spectrum of [math] consists of the eigenvalues of a symmetric matrix [math] of size [math], and at the most [math] and [math]. Also, we find the exact multiplicity of the eigenvalue [math] and show that all eigenvalues of [math] are nonzero, by determining the rank and nullity of the adjacency matrix of [math]. We find the values of [math] for which the adjacency spectrum of [math] contains only nonzero eigenvalues. Finally, by computing the characteristic polynomial of the matrix [math], we determine the characteristic polynomial of [math] whenever [math] is a prime power.
Citation: Journal of Algebra and Its Applications
PubDate: 20210705T07:00:00Z
DOI: 10.1142/S0219498822501973

 Groups whose noncommuting graph on a transversal is planar or toroidal

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Authors: Julio C. M. Pezzott
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a finite nonabelian group and let [math] be a transversal of the center of [math]. The noncommuting graph of [math] on a transversal of the center is the graph denoted by [math] whose vertices are the noncentral elements of [math] and two vertices [math] and [math] are joined by an edge whenever [math]. In this paper, we determine (up to isoclinism) all finite nonabelian groups whose noncommuting graph on a transversal of the center is planar or toroidal.
Citation: Journal of Algebra and Its Applications
PubDate: 20210705T07:00:00Z
DOI: 10.1142/S0219498822501985

 A basis of a certain module for the hyperalgebra of [math] and some
applications
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Authors: Yutaka Yoshii
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In the hyperalgebra [math] of the [math]th Frobenius kernel [math] of the algebraic group [math], we construct a basis of the [math]module generated by a certain element which was given by the author before. As its applications, we also prove some results on the [math]modules and the algebra [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210702T07:00:00Z
DOI: 10.1142/S0219498822501845

 Tensor products of finitely presented functors

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Authors: Martin Bies, Sebastian Posur
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We provide explicit constructions for various ingredients of right exact monoidal structures on the category of finitely presented functors. As our main tool, we prove a multilinear version of the universal property of socalled Freyd categories, which in turn is used in the proof of correctness of our constructions. Furthermore, we compare our construction with the Day convolution of arbitrary additive functors. Day convolution always yields a closed monoidal structure on the category of all additive functors. In contrast, right exact monoidal structures for finitely presented functor categories are not necessarily closed. We provide a necessary criterion for being closed that relies on the underlying category having weak kernels and a socalled finitely presented prointernal hom structure. Our results are stated in a constructive way and thus serve as a unified approach for the implementation of tensor products in various contexts.
Citation: Journal of Algebra and Its Applications
PubDate: 20210702T07:00:00Z
DOI: 10.1142/S0219498822501869

 Fully [math]coidempotent modules

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Authors: F. Farshadifar, H. AnsariToroghy
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative ring with identity, [math] be a multiplicatively closed subset of [math], and [math] be an [math]module. A submodule [math] of [math] is called coidempotent if [math]. Also, [math] is called fully coidempotent if every submodule of [math] is coidempotent. In this paper, we introduce the concepts of [math]coidempotent submodules and fully [math]coidempotent [math]modules as generalizations of coidempotent submodules and fully coidempotent [math]modules. We explore some basic properties of these classes of [math]modules.
Citation: Journal of Algebra and Its Applications
PubDate: 20210702T07:00:00Z
DOI: 10.1142/S0219498822502024

 Lie solvable Leavitt path algebras

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Authors: Tran Giang Nam, Zerui Zhang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We provide necessary and sufficient conditions on the graph [math] and the field [math] for which the Leavitt path algebra [math] is Lie solvable. Consequently, we obtain a complete description of Lie nilpotent Leavitt path algebras, and show that the Lie solvability of [math] and the Lie nilpotency of [math] are the same. Furthermore, we compute the solvable index of a Lie solvable Leavitt path algebra.
Citation: Journal of Algebra and Its Applications
PubDate: 20210702T07:00:00Z
DOI: 10.1142/S0219498822502036

 Certain homological invariants of bipartite kneser graphs

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Authors: Ajay Kumar, Pavinder Singh, Rohit Verma
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we obtain a combinatorial formula for computing the Betti numbers in the linear strand of edge ideals of bipartite Kneser graphs. We deduce lower and upper bounds for regularity of powers of edge ideals of these graphs in terms of associated combinatorial data and show that the lower bound is attained in some cases. Also, we obtain bounds on the projective dimension of edge ideals of these graphs in terms of combinatorial data.
Citation: Journal of Algebra and Its Applications
PubDate: 20210702T07:00:00Z
DOI: 10.1142/S0219498822502061

 A notion of rank for noncommutative quadratic forms on four generators

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Authors: Jessica G. Cain, Leah R. Frauendienst, Padmini Veerapen
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we extend work from [M. Vancliff and P. P. Veerapen, Generalizing the notion of rank to noncommutative quadratic forms, in Noncommutative Birational Geometry, Representations and Combinatorics, eds. A. Berenstein and V. Retakh, Contemporary Mathematics, Vol. 592 (2013), pp. 241–250], where a notion of rank, called [math]rank, was proposed for noncommutative quadratic forms on two and three generators. In particular, we provide a definition of [math]rank one and two for noncommutative quadratic forms on four generators. We apply this definition to determine the number of point modules over certain quadratic ASregular algebras of global dimension four.
Citation: Journal of Algebra and Its Applications
PubDate: 20210628T07:00:00Z
DOI: 10.1142/S0219498822501961

 Cotangent spaces and separating reembeddings

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Authors: Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Given an affine algebra [math], where [math] is a polynomial ring over a field [math] and [math] is an ideal in [math], we study reembeddings of the affine scheme [math], i.e. presentations [math] such that [math] is a polynomial ring in fewer indeterminates. To find such reembeddings, we use polynomials [math] in the ideal [math] which are coherently separating in the sense that they are of the form [math] with an indeterminate [math] which divides neither a term in the support of [math] nor in the support of [math] for [math]. The possible numbers of such sets of polynomials are shown to be governed by the Gröbner fan of [math]. The dimension of the cotangent space of [math] at a [math]linear maximal ideal is a lower bound for the embedding dimension, and if we find coherently separating polynomials corresponding to this bound, we know that we have determined the embedding dimension of [math] and found an optimal reembedding.
Citation: Journal of Algebra and Its Applications
PubDate: 20210622T07:00:00Z
DOI: 10.1142/S0219498822501882

 On [math]embedded subgroups of finite groups

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Authors: Yaxin Gao, Xianhua Li
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a finite group and [math] a subgroup of [math]. [math] is said to be [math]embedded in [math] if there exists a normal subgroup [math] of [math] such that [math] is a Hall subgroup of [math] and [math], where [math] is the largest [math]semipermutable subgroup of [math] contained in [math]. In this paper, we give some new characterizations of [math]nilpotent and supersolvable groups by using [math]embedded subgroups. Some known results are generalized.
Citation: Journal of Algebra and Its Applications
PubDate: 20210622T07:00:00Z
DOI: 10.1142/S0219498822502000

 Copure direct injective modules

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Authors: Sanjeev Kumar Maurya, Sultan Eylem Toksoy
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we have introduced copuredirectinjective modules. A right [math]module [math] is said to be copuredirectinjective if every copure submodule of [math] isomorphic to a direct summand of [math] is itself a direct summand. We have studied properties of copuredirectinjective modules. We characterized rings over which every (cofinitely generated, free, projective) module is copuredirectinjective. We have examined for which rings or under what conditions copuredirectinjective modules are directinjective, quasiinjective, copureinjective, injective. Also we have compared copuredirectinjective modules with puredirectinjective modules.
Citation: Journal of Algebra and Its Applications
PubDate: 20210619T07:00:00Z
DOI: 10.1142/S0219498822501870

 A link between minimal value set polynomials and tamely ramified towers of
function fields over finite fields
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Authors: R. Toledano
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduce the notions of [math]polynomial and [math]minimal value set polynomial where [math] is a polynomial over a finite field [math] and [math] is a finite subset of an algebraic closure of [math]. We study some properties of these polynomials and we prove that the polynomials used by Garcia, Stichtenoth and Thomas in their work on good recursive tame towers are [math]minimal value set polynomials for [math], whose [math]value sets can be explicitly computed in terms of the monomial [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210619T07:00:00Z
DOI: 10.1142/S0219498822501894

 Inverse complements and strongly unit regular elements

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Authors: Umashankara Kelathaya, Savitha Varkady, Manjunatha Prasad Karantha
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, the notion of “strongly unit regular element”, for which every reflexive generalized inverse is associated with an inverse complement, is introduced. Noting that every strongly unit regular element is unit regular, some characterizations of unit regular elements are obtained in terms of inverse complements and with the help of minus partial order. Unit generalized inverses of given unit regular element are characterized as sum of reflexive generalized inverses and the generators of its annihilators. Surprisingly, it has been observed that the class of strongly regular elements and unit regular elements are the same. Also, several classes of generalized inverses are characterized in terms of inverse complements.
Citation: Journal of Algebra and Its Applications
PubDate: 20210619T07:00:00Z
DOI: 10.1142/S0219498822501900

 The Hilbert series of the irreducible quotient of the polynomial
representation of the rational Cherednik algebra of type [math] in
characteristic [math] for [math]
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Authors: Merrick Cai, Daniil Kalinov
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we study the irreducible quotient [math] of the polynomial representation of the rational Cherednik algebra [math] of type [math] over an algebraically closed field of positive characteristic [math] where [math]. In the [math] case, for all [math] we give a complete description of the polynomials in the maximal proper graded submodule [math], the kernel of the contravariant form [math], and subsequently find the Hilbert series of the irreducible quotient [math]. In the [math] case, we give a complete description of the polynomials in [math] when the characteristic [math] and [math] is transcendental over [math], and compute the Hilbert series of the irreducible quotient [math]. In doing so, we prove a conjecture due to Etingof and Rains completely for [math], and also for any [math] and [math]. Furthermore, for [math], we prove a simple criterion to determine whether a given polynomial [math] lies in [math] for all [math] with [math] and [math] fixed.
Citation: Journal of Algebra and Its Applications
PubDate: 20210619T07:00:00Z
DOI: 10.1142/S0219498822501912

 Notes on resolving resolution dimensions

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Authors: Aimin Xu
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an abelian category and [math] be two quasiresolving subcategories of [math], where [math] is closed under direct summands and [math] is a cogenerator for [math]. For any [math], it is shown that [math][math][math]. Some examples and applications are also given.
Citation: Journal of Algebra and Its Applications
PubDate: 20210619T07:00:00Z
DOI: 10.1142/S0219498822501948

 On strongly dccr[math] modules

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Authors: Osama A. Naji, Mehmet Özen, Unsal Tekir
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduce and study the concept of strongly dccr[math] modules. Strongly dccr[math] condition generalizes the class of Artinian modules and it is stronger than dccr[math] condition. Let [math] be a commutative ring with nonzero identity and [math] a unital [math]module. A module [math] is said to be strongly [math] if for every submodule [math] of [math] and every sequence of elements [math] of [math], the descending chain of submodules [math] of [math] is stationary. We give many examples and properties of strongly dccr[math]. Moreover, we characterize strongly dccr[math] in terms of some known class of rings and modules, for instance in perfect rings, strongly special modules and principally cogenerately modules. Finally, we give a version of Union Theorem and Nakayama’s Lemma in light of strongly dccr[math] concept.
Citation: Journal of Algebra and Its Applications
PubDate: 20210619T07:00:00Z
DOI: 10.1142/S021949882250195X

 The Grothendieck rings of Wu–Liu–Ding algebras and their
Casimir numbers (I)
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Authors: Ruifang Yang, Shilin Yang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Wu–Liu–Ding algebras are a class of affine prime regular Hopf algebras of GKdimension one, denoted by [math]. In this paper, we consider their quotient algebras [math] which are a new class of nonpointed semisimple Hopf algebras. We describe the Grothendieck rings of [math] when [math] is odd. It turns out that the Grothendieck rings are commutative rings generated by three elements subject to some relations. Then we compute the Casimir numbers of the Grothendieck rings for [math] and [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210617T07:00:00Z
DOI: 10.1142/S021949882250178X

 Degrees of faithful irreducible representations of metabelian groups

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Authors: Rahul Dattatraya Kitture, Soham Swadhin Pradhan
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In 1993, Sim proved that all the faithful irreducible representations of a finite metacyclic group over any field of positive characteristic have the same degree. In this paper, we restrict our attention to nonmodular representations and generalize this result for — (1) finite metabelian groups, over fields of positive characteristic coprime to the order of groups, and (2) finite groups having a cyclic quotient by an abelian normal subgroup, over number fields.
Citation: Journal of Algebra and Its Applications
PubDate: 20210617T07:00:00Z
DOI: 10.1142/S021949882250181X

 On the projectivity of proper normal curves over valuation domains

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Authors: Hagen Knaf
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
A theorem of Lichtenbaum states, that every proper, regular curve [math] over a discrete valuation domain [math] is projective. This theorem is generalized to the case of an arbitrary valuation domain [math] using the following notion of regularity for nonnoetherian rings introduced by Bertin: the local ring [math] of a point [math] is called regular, if every finitely generated ideal [math] has finite projective dimension. The generalization is a particular case of a projectivity criterion for proper, normal [math]curves: such a curve [math] is projective if for every irreducible component [math] of its closed fiber [math] there exists a closed point [math] of the generic fiber of [math] such that the Zariski closure [math] meets [math] and meets [math] in regular points only.
Citation: Journal of Algebra and Its Applications
PubDate: 20210617T07:00:00Z
DOI: 10.1142/S0219498822501833

 Anderson [math]motives and abelian varieties with MIQF: Results coming
from an analogy
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Authors: A. Grishkov, D. Logachev
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Analogy between Anderson [math]motives and abelian varieties with multiplication by an imaginary quadratic field (MIQF) is a source of 2 results: (1) A description of abelian varieties with MIQF of dimension [math] and signature [math] in terms of ”lattices” of dimension [math] in [math]; (2) A construction of exterior powers of abelian varieties with MIQF having [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210615T07:00:00Z
DOI: 10.1142/S0219498822501717

 The compressed zerodivisor graphs of order 4

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Authors: A. S. Monastyreva
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In [E. V. Zhuravlev and A. S. Monastyreva, Compressed zerodivisor graphs of finite associative rings, Siberian Math. J. 61(1) (2020) 76–84.], we found the graphs containing at most three vertices that can be realized as the compressed zerodivisor graphs of some finite associative ring. This paper deals with associative finite rings whose compressed zerodivisor graphs have four vertices. Namely, we find all graphs containing four vertices that can be realized as the compressed zerodivisor graphs of some finite associative ring.
Citation: Journal of Algebra and Its Applications
PubDate: 20210615T07:00:00Z
DOI: 10.1142/S0219498822501791

 On rings with cyclic almostinjective modules

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Authors: Adel Nailevich Abyzov, Truong Cong Quynh
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
It is shown that every finitely generated right [math]module is almost injective if and only if every cyclic right [math]module is almost injective, if and only if [math] is a right [math]ring with [math] and there is a finite set of orthogonal idempotents [math] in [math] such that [math] is an injective local right [math]module of length two for every [math] and [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210615T07:00:00Z
DOI: 10.1142/S0219498822501808

 On the relation between torsion submodule and Fitting ideals

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Authors: S. Hadjirezaei
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative ring and let [math] be a submodule of [math] which consists of columns of a matrix [math] with [math] for all [math], [math], where [math] is an index set. For every [math], let I[math] be the ideal generated by subdeterminants of size [math] of the matrix [math]. Let [math]. In this paper, we obtain a constructive description of [math] and we show that when [math] is a local ring, [math] is free of rank [math] if and only if I[math] is a principal regular ideal, for some [math]. This improves a lemma of Lipman which asserts that, if [math] is the [math]th Fitting ideal of [math] then [math] is a regular principal ideal if and only if [math] is finitely generated free and [math] is free of rank [math]
Citation: Journal of Algebra and Its Applications
PubDate: 20210614T07:00:00Z
DOI: 10.1142/S0219498822501730

 Stability conditions and braid group actions on affine [math] quivers

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Authors: ChienHsun Wang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We study stability conditions on the Calabi–Yau[math] categories associated to an affine type [math] quiver which can be constructed from certain meromorphic quadratic differentials with zeroes of order [math]. We follow Ikeda’s work to show that this moduli space of quadratic differentials is isomorphic to the space of stability conditions quotient by the spherical subgroup of the autoequivalence group. We show that the spherical subgroup is isomorphic to the braid group of affine type [math] based on the Khovanov–Seidel–Thomas method.
Citation: Journal of Algebra and Its Applications
PubDate: 20210609T07:00:00Z
DOI: 10.1142/S0219498822501742

 Structure of sympathetic 3Lie algebras

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Authors: Chenrui Yao, Liangyun Chen
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we will introduce the concept of sympathetic [math]Lie algebras and show that some classical properties of semisimple [math]Lie algebras are still valid for sympathetic [math]Lie algebras. We prove that every perfect [math]Lie algebra [math] contains a greatest special sympathetic ideal [math], and there exists a solvable ideal of [math] denoted by [math] which is the greatest among the solvable ideals [math] of [math] for which [math]. And we show that there exists a sympathetic subalgebra [math] of [math] such that [math] and [math] is a sympathetic [math]Lie algebra if and only if [math]. Moreover, we also study the ideals [math] of a [math]Lie algebra [math] such that [math] is a sympathetic [math]Lie algebra and investigate some properties about them.
Citation: Journal of Algebra and Its Applications
PubDate: 20210609T07:00:00Z
DOI: 10.1142/S0219498822501857

 On power invariant rings

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Authors: Mohamed Khalifa
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative ring with identity, [math] be an indeterminate and [math] be the set of elements [math] of [math] such that there exists an [math]homomorphism of rings [math] with [math]. O’Malley called [math] to be power invariant (respectively, strongly power invariant) if whenever [math] is a ring such that [math] is isomorphic to [math] (respectively, whenever [math] is a ring and [math] is an isomorphism of [math] onto [math]), then [math] and [math] are isomorphic (respectively, then there exists an [math]automorphism [math] of [math] such that [math]) [M. O’Malley, Isomorphic power series rings, Pacific J. Math. 41(2) (1972) 503–512]. We prove that a ring [math] is power invariant in each of the following case: [math] [math] is a domain in which [math] is comparable to each radical ideal of [math] (for instance a domain with Krull dimension one), [math] [math] is a domain in which Jac[math] (i.e. the Jacobson radical of [math]) is comparable to each radical ideal of [math] and [math] [math] is a Prüfer domain. Also in each of the aforementioned case, we prove that either [math] is strongly power invariant or [math] is isomorphic to a quasilocal power series ring. Let [math] be a unital module over [math]. We show that if [math] is reduced and strongly power invariant, then Nagata’s idealization ring [math] is strongly power invariant (but the converse is false). Ishibashi called a ring [math] to be strongly[math]power invariant if whenever [math] is a ring and [math] is an isomorphism of [math] onto [math], then there exists an [math]automorphism [math] of [math] such that [math] for each [math]. We prove that if [math] is a ring in which [math] is nil, then [math] is strongly[math]power invariant for all positive integer [math]. We deduce that every polynomial ring in finitely many indeterminates is strongly[math]power invariant for all positive integer [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210603T07:00:00Z
DOI: 10.1142/S021949882250164X

 Cohomology and extensions of ordered groupoids

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Authors: B. O. Bainson, N. D. Gilbert
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We adapt and generalize results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a fiveterm exact sequence in cohomology from an extension of ordered groupoids, and show that this sequence leads to a classification of extensions by a second cohomology group. Our methods use structural ideas in cohomology as far as possible, rather than computation with cocycles.
Citation: Journal of Algebra and Its Applications
PubDate: 20210603T07:00:00Z
DOI: 10.1142/S0219498822501778

 The nonabelian tensor and exterior products of crossed modules of Lie
superalgebras
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Authors: Tahereh Fakhr Taha, Manuel Ladra, Pilar PáezGuillán
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduce the notions of nonabelian tensor and exterior products of two ideal graded crossed submodules of a given crossed module of Lie superalgebras. We also study some of their basic properties and their connection with the second homology of crossed modules of Lie superalgebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20210531T07:00:00Z
DOI: 10.1142/S0219498822501699

 A note on absolutevalued algebras satisfying [math]

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Authors: Kandé Diaby, Abdellatif Rochdi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We study the absolutevalued algebras [math] satisfying the identity [math] We show that, if moreover, the norm of [math] comes from an inner product and [math] contains a nonzero central element then [math] is finite dimensional and isomorphic to either [math] or [math]
Citation: Journal of Algebra and Its Applications
PubDate: 20210526T07:00:00Z
DOI: 10.1142/S0219498822501729

 Lie polynomials in an algebra defined by a linearly twisted commutation
relation
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Authors: Rafael Reno S. Cantuba
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We present an elementary approach to characterizing Lie polynomials on the generators [math] of an algebra with a defining relation in the form of a twisted commutation relation [math]. Here, the twisting map [math] is a linear polynomial with a slope parameter, which is not a root of unity. The class of algebras defined as such encompasses [math]deformed Heisenberg algebras, rotation algebras, and some types of [math]oscillator algebras, the deformation parameters of which, are not roots of unity. Thus, we have a general solution for the Lie polynomial characterization problem for these algebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20210526T07:00:00Z
DOI: 10.1142/S0219498822501754

 Semirigid GCD domains II

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Authors: M. Zafrullah
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be an integral domain with quotient field [math] throughout[math] Call two elements [math][math]coprime if [math] Call a nonzero nonunit [math] of an integral domain [math] rigid if for all [math] we have [math] or [math] Also, call [math] semirigid if every nonzero nonunit of [math] is expressible as a finite product of rigid elements. We show that a semirigid domain [math] is a GCD domain if and only if [math] satisfies [math] product of every pair of non[math]coprime rigid elements is again rigid. Next, call [math] a valuation element if [math] for some valuation ring [math] with [math] and call [math] a VFD if every nonzero nonunit of [math] is a finite product of valuation elements. It turns out that a valuation element is what we call a packed element: a rigid element [math] all of whose powers are rigid and [math] is a prime ideal. Calling [math] a semipacked domain (SPD) if every nonzero nonunit of [math] is a finite product of packed elements, we study SPDs and explore situations in which a variant of an SPD is a semirigid GCD domain.
Citation: Journal of Algebra and Its Applications
PubDate: 20210525T07:00:00Z
DOI: 10.1142/S0219498822501614

 PseudoSylvester domains and skew laurent polynomials over firs

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Authors: Fabian Henneke, Diego LópezÁlvarez
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Building on recent work of JaikinZapirain, we provide a homological criterion for a ring to be a pseudoSylvester domain, that is, to admit a division ring of fractions over which all stably full matrices become invertible. We use the criterion to study skew Laurent polynomial rings over free ideal rings (firs). As an application of our methods, we prove that crossed products of division rings with freeby{infinite cyclic} and surface groups are pseudoSylvester domains unconditionally and Sylvester domains if and only if they admit stably free cancellation. This relies on the recent proof of the Farrell–Jones conjecture for normally polyfree groups and extends previous results of Linnell–Lück and JaikinZapirain on universal localizations and universal fields of fractions of such crossed products.
Citation: Journal of Algebra and Its Applications
PubDate: 20210525T07:00:00Z
DOI: 10.1142/S0219498822501687

 On the structure of finite groups with dominatable enhanced power graph

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Authors: A. Mahmoudifar, A. Babai
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a group. The enhanced power graph of [math] is a graph with vertex set [math] and two distinct vertices [math] and [math] are adjacent if there exists [math] such that [math] and [math] for some [math]. Also, a vertex of a graph is called dominating vertex if it is adjacent to every other vertex of the vertex set. Moreover, an enhanced power graph is said to be a dominatable graph if it has a dominating vertex other than the identity element. In an article of 2018, Bera and his coauthor characterized all abelian finite groups and nonabelian finite [math]groups such that their enhanced power graphs are dominatable (see [2]). In addition as an open problem, they suggested characterizing all finite nonabelian groups such that their enhanced power graphs are dominatable. In this paper, we try to answer their question. We prove that the enhanced power graph of finite group [math] is dominatable if and only if there is a prime number [math] such that [math] and the Sylow [math]subgroups of [math] are isomorphic to either a cyclic group or a generalized quaternion group.
Citation: Journal of Algebra and Its Applications
PubDate: 20210525T07:00:00Z
DOI: 10.1142/S0219498822501766

 Isotropy groups of free racks and quandles

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Authors: Jason Parker
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we characterize the (covariant) isotropy groups of free, finitely generated racks and quandles. As a consequence, we show that the usual inner automorphisms of such racks and quandles are precisely those automorphisms that are “coherently extendible”. We then use this result to compute the global isotropy groups of the categories of racks and quandles, i.e. the automorphism groups of the identity functors of these categories.
Citation: Journal of Algebra and Its Applications
PubDate: 20210521T07:00:00Z
DOI: 10.1142/S0219498822501638

 Lie centralizers at the zero products on generalized matrix algebras

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Authors: B. Fadaee, H. Ghahramani
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a 2torsion free unital generalized matrix algebra, and [math] be a linear map satisfying S,T ∈ð’°,ST = 0 ⇒ ϕ([S,T]) = [ϕ(S),T] = [S,ϕ(T)]. In this paper, we study the structure of [math] and under some mild conditions on [math] we present the necessary and sufficient conditions for [math] to be in terms of centralizers. We then provide the characterizations of Lie centralizers on [math] and our results generalize some of the previous results. We also refer to some applications of our results for triangular algebras and some operator algebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20210521T07:00:00Z
DOI: 10.1142/S0219498822501651

 Green’s relation [math] on the monoid of square matrices over a
specific local ring
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Authors: Nan Wangyu, Yang Jiang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative local ring whose maximal ideal is generated by a nilpotent element, and [math] be the multiplicative monoid of the square matrices of order [math] over [math]. In this paper, we provide the construction of Green’s [math]equivalence classes in the multiplicative monoid [math]. Then, we enumerate these classes in the special cases [math] and [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210521T07:00:00Z
DOI: 10.1142/S0219498822501705

 FGpurity and FGflat modules

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Authors: James Gillespie
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a ring. We study the FGpure exact sequences, which are defined analogously to pure exact sequences except with respect to finitely generated [math]modules rather than the finitely presented [math]modules. For Noetherian rings the two notions coincide. But for nonNoetherian rings, the FGpurity is sharper than the usual purity. We also study the corresponding notion of FGflat module and construct a model for the FGpure derived category. It is a compactly generated triangulated category.
Citation: Journal of Algebra and Its Applications
PubDate: 20210518T07:00:00Z
DOI: 10.1142/S0219498822501675

 Commutative rings with invertibleradical factorization

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Authors: Malik Tusif Ahmed, Najib Mahdou, Youssef Zahir
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties under homomorphic image and their transfer to various contexts of constructions such as direct product, trivial ring extension and amalgamated duplication of a ring along an ideal. Our results generate examples that enrich the current literature with new and original families of rings satisfying these properties.
Citation: Journal of Algebra and Its Applications
PubDate: 20210507T07:00:00Z
DOI: 10.1142/S0219498822501535

 Rings all of whose finitely generated ideals are automorphisminvariant

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Authors: Truong Cong Quynh, Adel Nailevich Abyzov, Dao Thi Trang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Rings in which each finitely generated right ideal is automorphisminvariant (right[math]rings) are shown to be isomorphic to a formal matrix ring. Among other results it is also shown that (i) if [math] is a right nonsingular ring and [math] is an integer, then [math] is a right self injective regular ring if and only if the matrix ring [math] is a right [math]ring, if and only if [math] is a right automorphisminvariant ring and (ii) a right nonsingular ring [math] is a right [math]ring if and only if [math] is a direct sum of a squarefull von Neumann regular right selfinjective ring and a strongly regular ring containing all invertible elements of its right maximal ring of fractions. In particular, we show that a right semiartinian (or left semiartinian) ring [math] is a right nonsingular right [math]ring if and only if [math] is a left nonsingular left [math]ring.
Citation: Journal of Algebra and Its Applications
PubDate: 20210507T07:00:00Z
DOI: 10.1142/S0219498822501596

 Gradings allowing wild automorphisms

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Authors: Anton Trushin
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In 2004, Shestakov and Umirbaev proved that the Nagata automorphism of the polynomial algebra in three variables is wild. We fix a [math]grading on this algebra and consider gradedwild automorphisms, i.e. such automorphisms that cannot be decomposed onto elementary automorphisms respecting the grading. We describe all gradings allowing gradedwild automorphisms.
Citation: Journal of Algebra and Its Applications
PubDate: 20210507T07:00:00Z
DOI: 10.1142/S0219498822501602

 On canonical bases of a formal [math]algebra

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Authors: Abdallah Assi
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We study canonical bases of a subalgebra [math] over a field [math], and we associate with [math] a fan called the canonical fan of [math]. This generalizes the notion of the standard fan of an ideal.
Citation: Journal of Algebra and Its Applications
PubDate: 20210507T07:00:00Z
DOI: 10.1142/S0219498822501626

 Classpreserving Coleman automorphisms of finite groups whose Sylow
2subgroups are semidihedral
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Authors: Tao Zheng, Xiuyun Guo
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we mainly investigate the classpreserving Coleman automorphisms of finite groups whose Sylow 2subgroups are semidihedral. We prove that if [math] is a finite solvable group with semidihedral Sylow 2subgroups, then [math] is a [math]group and therefore [math] satisfies the normalizer property. As some applications of this result, we also investigate the normalizer property of the following groups: the groups whose Sylow 2subgroups are semidihedral and Sylow subgroups of odd order are all cyclic, the groups [math] with [math] a nilpotent normal subgroup and [math] a maximal class 2group, and the wreath products [math] with [math] a group whose Sylow 2subgroups are of maximal class with order [math] and [math] a rational permutation group.
Citation: Journal of Algebra and Its Applications
PubDate: 20210507T07:00:00Z
DOI: 10.1142/S0219498822501663

 Some results on formal local cohomology

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Authors: Tran Tuan Nam, Tran Le Quyen, Nguyen Hoang Huy Tu, Nguyen Minh Tri
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We study some properties of formal local cohomology modules [math] in Serre subcategories. As a consequence, we obtain some results on the minimax modules. We also describe the sets [math] and [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210504T07:00:00Z
DOI: 10.1142/S0219498822501493

 Left nondegenerate settheoretic solutions of the Yang–Baxter equation
and dynamical extensions of qcycle sets
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Authors: Marco Castelli, Francesco Catino, Paola Stefanelli
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
A first aim of this paper is to give sufficient conditions on left nondegenerate bijective settheoretic solutions of the Yang–Baxter equation so that they are nondegenerate. In particular, we extend the results on involutive solutions obtained by Rump in A decomposition theorem for squarefree unitary solutions of the quantum Yang–Baxter equation, Adv. Math. 193 (2005) 40–55, https://doi.org/10.1016/j.aim.2004.03.019 and answer positively a question posed by Cedó et al. in Question 4.2 in Structure monoids of settheoretic solutions of the Yang–Baxter equation, preprint (2019), https://arxiv.org/abs/1912.09710. Moreover, we develop a theory of extensions for left nondegenerate settheoretic solutions of the Yang–Baxter equation that allows one to construct new families of settheoretic solutions.
Citation: Journal of Algebra and Its Applications
PubDate: 20210504T07:00:00Z
DOI: 10.1142/S0219498822501547

 The Bochner–Schoenberg–Eberlein property for amalgamated
duplication of Banach algebras
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Authors: Ali Ebadian, Ali Jabbari
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
The Bochner–Schoenberg–Eberlein (BSE)property on commutative Banach algebras is a property related to multiplier algebras of Banach algebras. In this paper, we answer the problem (12) raised by Javanshiri and Nemati in [Amalgamated duplication of the Banach algebra [math] along a [math]bimodule [math], J. Algebra Appl. 17(9) (2018) 18501691–185016921]. In this paper, under certain conditions, we show that the amalgamated Banach algebra [math] is BSEalgebra if and only if [math] and [math] are BSEalgebras.
Citation: Journal of Algebra and Its Applications
PubDate: 20210504T07:00:00Z
DOI: 10.1142/S0219498822501559

 Absence of torsion in orbit space

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Authors: Sampat Sharma
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we prove that if [math] is a local ring of dimension [math] [math] and [math] then the group [math] has no [math]torsion, provided [math] We also prove that if [math] is a regular ring of dimension [math] [math] and [math] such that [math] acts transitively on [math] then [math] acts transitively on [math]
Citation: Journal of Algebra and Its Applications
PubDate: 20210504T07:00:00Z
DOI: 10.1142/S0219498822501572

 Kernels of homomorphisms between uniform quasiinjective modules

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Authors: M. Tamer Koşan, Truong Cong Quynh, Jan Žemlička
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we study the behavior of endomorphism rings of indecomposable (uniform) quasiinjective modules. A very natural question here is, for a morphism [math], with [math] indecomposable (uniform) quasiinjective right [math]modules, and [math] an extension of [math] where [math] denotes the injective hull, what is the relation between kernels of [math] and [math], their monogeny classes and their upper parts'
Citation: Journal of Algebra and Its Applications
PubDate: 20210504T07:00:00Z
DOI: 10.1142/S0219498822501584

 Modules whose injectivity domains are restricted to semiartinian modules

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Authors: Shahabaddin Ebrahimi Atani, Mehdi Khoramdel, Saboura Dolati Pish Hesari
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We introduce the notion of semipoor modules and consider the possibility that all modules are either injective or semipoor. This notion gives a generalization of poor modules that have minimal injectivity domain. A module [math] is called semipoor if whenever it is [math]injective and [math], then the module [math] has nonzero socle. In this paper the properties of semipoor modules are investigated and are used to characterize various families of rings. We introduce the rings over which every module is either semipoor or injective and call such condition property [math]. The structure of the rings that have the property [math] is completely determined. Also, we give some characterizations of rings with the property [math] in the language of the lattice of hereditary pretorsion classes over a given ring. It is proved that a ring [math] has the property [math] iff either [math] is right semiArtinian or [math] where [math] is a semisimple Artinian ring and [math] is right strongly prime and a right [math]ring with zero right socle.
Citation: Journal of Algebra and Its Applications
PubDate: 20210429T07:00:00Z
DOI: 10.1142/S021949882250150X

 IC rings and transitivity of perspectivity

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Authors: Xavier Mary, Pace P. Nielsen
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We construct an example of an IC ring where perspectivity is transitive, but not all isomorphic idempotents are perspective. We also develop new criteria for checking perspectivity of idempotents in rings.
Citation: Journal of Algebra and Its Applications
PubDate: 20210429T07:00:00Z
DOI: 10.1142/S0219498822501511

 Homological dimensions of special modules over formal triangular matrix
rings
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Authors: Lixin Mao
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a formal triangular matrix ring, where [math] and [math] are rings and [math] is a [math]bimodule. We give some computing formulas of homological dimensions of special [math]modules. As an application, we describe the structures of [math]tilting left [math]modules.
Citation: Journal of Algebra and Its Applications
PubDate: 20210423T07:00:00Z
DOI: 10.1142/S0219498822501468

 Hochschild cohomology, finiteness conditions and a generalization of
[math]Koszul algebras
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Authors: Ruaa Jawad, Nicole Snashall
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Given a finitedimensional algebra [math] and [math], we construct a new algebra [math], called the stretched algebra, and relate the homological properties of [math] and [math]. We investigate Hochschild cohomology and the finiteness condition (Fg), and use stratifying ideals to show that [math] has (Fg) if and only if [math] has (Fg). We also consider projective resolutions and apply our results in the case where [math] is a [math]Koszul algebra for some [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210423T07:00:00Z
DOI: 10.1142/S021949882250147X

 Quasimultipliers on topological semigroups and their
Stone–Čech compactification
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Authors: A. Alinejad, M. Essmaili, M. Rostami
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduce and study the notion of quasimultipliers on a semitopological semigroup [math]. The set of all quasimultipliers on [math] is denoted by [math]. First, we study the problem of extension of quasimultipliers on topological semigroups to its Stone–Čech compactification. Indeed, we prove if [math] is a topological semigroup such that [math] is pseudocompact, then [math] can be regarded as a subset of [math] Moreover, with an extra condition we describe [math] as a quotient subsemigroup of [math] Finally, we investigate quasimultipliers on topological semigroups, its relationship with multipliers and give some concrete examples.
Citation: Journal of Algebra and Its Applications
PubDate: 20210423T07:00:00Z
DOI: 10.1142/S0219498822501481

 Reducibility index and sumreducibility index

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Authors: Tran Nguyen An, Tran Duc Dung, Shinya Kumashiro, Le Thanh Nhan
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a commutative Noetherian ring. For a finitely generated [math]module [math], Northcott introduced the reducibility index of [math], which is the number of submodules appearing in an irredundant irreducible decomposition of the submodule [math] in [math]. On the other hand, for an Artinian [math]module [math], Macdonald proved that the number of sumirreducible submodules appearing in an irredundant sumirreducible representation of [math] does not depend on the choice of the representation. This number is called the sumreducibility index of [math]. In the former part of this paper, we compute the reducibility index of [math], where [math] is a flat homomorphism of Noetherian rings. Especially, the localization, the polynomial extension, and the completion of [math] are studied. For the latter part of this paper, we clarify the relation among the reducibility index of [math], that of the completion of [math], and the sumreducibility index of the Matlis dual of [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210423T07:00:00Z
DOI: 10.1142/S0219498822501523

 On [math]property of subgroups of a finite group

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Authors: Xinwei Wu, Xianhua Li
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a finite group, [math] a prime, [math] a Sylow [math]subgroup of [math] and [math] a power of [math] such that [math]. Let [math] denote the unique smallest normal subgroup of [math] for which the corresponding factor group is abelian of exponent dividing [math]. Let [math], [math], [math] be classes of all [math]groups, [math]nilpotent groups and [math]supersolvable groups, respectively, [math] be the [math]residual of [math]. Let [math]. A subgroup [math] of a finite group [math] is said to have [math]property in [math], if for any [math]chief factor [math], [math] is a [math]number. A normal subgroup [math] of [math] is said to be [math]hypercyclically embedded in [math] if every [math][math]chief factor of [math] is cyclic, where [math] is a fixed prime. In this paper, we prove that [math] is [math]hypercyclically embedded in [math] if and only if for some [math]subgroups [math] of [math], [math] have [math]property in [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210423T07:00:00Z
DOI: 10.1142/S0219498822501560

 Strongly graded Leavitt path algebras

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Authors: Patrik Lundström, Johan Öinert
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Let [math] be a unital ring, let [math] be a directed graph and recall that the Leavitt path algebra [math] carries a natural [math]gradation. We show that [math] is strongly [math]graded if and only if [math] is rowfinite, has no sink, and satisfies Condition (Y). Our result generalizes a recent result by Clark, Hazrat and Rigby, and the proof is short and selfcontained.
Citation: Journal of Algebra and Its Applications
PubDate: 20210419T07:00:00Z
DOI: 10.1142/S0219498822501419

 Wellrounded twists of ideal lattices from imaginary quadratic fields

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Authors: Nam H. Le, Dat T. Tran, Ha T. N. Tran
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we investigate the properties of wellrounded twists of a given ideal lattice of an imaginary quadratic field [math]. We show that every ideal lattice [math] of [math] has at least one wellrounded twist lattice. Moreover, we provide an explicit algorithm to compute all wellrounded twists of [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210408T07:00:00Z
DOI: 10.1142/S021949882250133X

 Braided Rota–Baxter algebras, quantum quasishuffle algebras and
braided dendriform algebras
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Authors: Yunnan Li, Li Guo
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
Rota–Baxter algebras and the closely related dendriform algebras have important physics applications, especially to renormalization of quantum field theory. Braided structures provide effective ways of quantization such as for quantum groups. Continuing recent study relating the two structures, this paper considers Rota–Baxter algebras and dendriform algebras in the braided contexts. Applying the quantum shuffle and quantum quasishuffle products, we construct free objects in the categories of braided Rota–Baxter algebras and braided dendriform algebras, under the commutativity condition. We further generalize the notion of dendriform Hopf algebra to the braided context and show that quantum shuffle algebra gives a braided dendriform Hopf algebra. Enveloping braided commutative Rota–Baxter algebras of braided commutative dendriform algebras are obtained.
Citation: Journal of Algebra and Its Applications
PubDate: 20210408T07:00:00Z
DOI: 10.1142/S0219498822501341

 Type IV codes over a nonunital ring

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Authors: Adel Alahmadi, Alaa Altassan, Widyan Basaffar, Hatoon Shoaib, Alexis Bonnecaze, Patrick Solé
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
There is a special local ring [math] of order [math] without identity for the multiplication, defined by [math] We study the algebraic structure of linear codes over that noncommutative local ring, in particular their residue and torsion codes. We introduce the notion of quasi selfdual codes over [math] and Type IV codes, that is quasi selfdual codes whose all codewords have even Hamming weight. We study the weight enumerators of these codes by means of invariant theory, and classify them in short lengths.
Citation: Journal of Algebra and Its Applications
PubDate: 20210408T07:00:00Z
DOI: 10.1142/S0219498822501420

 The buildup construction of quasi selfdual codes over a nonunital ring

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Authors: Adel Alahmadi, Alaa Altassan, Hatoon Shoaib, Amani Alkathiry, Alexis Bonnecaze, Patrick Solé
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
There is a local ring [math] of order [math] without identity for the multiplication, defined by generators and relations as E = 〈a,b 2a = 2b = 0,a2 = a,b2 = b,ab = a,ba = b〉. We study a recursive construction of selforthogonal codes over [math] We classify, up to permutation equivalence, selforthogonal codes of length [math] and size [math] (called here quasi selfdual codes or QSD) up to the length [math]. In particular, we classify Type IV codes (QSD codes with even weights) up to [math].
Citation: Journal of Algebra and Its Applications
PubDate: 20210408T07:00:00Z
DOI: 10.1142/S0219498822501432

 On strongly [math]Noetherian rings

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Authors: Esmaeil Rostami
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduce a class of commutative rings which is a generalization of ZDrings and rings with Noetherian spectrum. A ring [math] is called strongly[math]Noetherian whenever the ring [math] is [math]Noetherian for every nonnilpotent [math]. We give some characterizations for strongly [math]Noetherian rings and, among the other results, we show that if [math] is strongly [math]Noetherian, then [math] has Noetherian spectrum, which is a generalization of Theorem 2 in Gilmer and Heinzer [The Laskerian property, power series rings, and Noetherian spectra, Proc. Amer. Math. Soc. 79 (1980) 13–16].
Citation: Journal of Algebra and Its Applications
PubDate: 20210408T07:00:00Z
DOI: 10.1142/S0219498822501444

 A note on the rightleft symmetry of [math] in rings

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Authors: TsiuKwen Lee
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We give an example to show that, for nonunital rings [math], the direct sum [math] with [math] regular has no in general rightleft symmetry. It is then proved that the rightleft symmetry actually holds in a left and right faithful ring.
Citation: Journal of Algebra and Its Applications
PubDate: 20210408T07:00:00Z
DOI: 10.1142/S0219498822501456

 Crossed modules for Hom–Lie antialgebras

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Authors: Tao Zhang, Heyu Zhang
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduced the concept of crossed modules for Hom–Lie antialgebras. It is proved that the category of crossed modules for Hom–Lie antialgebras and the category of [math]Hom–Lie antialgebras are equivalent to each other. The relationship between the crossed modules extension of Hom–Lie antialgebras and the third cohomology group is investigated.
Citation: Journal of Algebra and Its Applications
PubDate: 20210405T07:00:00Z
DOI: 10.1142/S0219498822501353

 ∗Almost superhomogeneous ideals in ∗[math]local domains

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Authors: Shiqi Xing, D. D. Anderson, Muhammad Zafrullah
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
In this paper, we introduce ∗almost independent rings of Krull type (∗almost IRKTs) and ∗almost generalized Krull domains (∗almost GKDs) in the general theory of almost factoriality, neither of which need be integrally closed. This fills a gap left in [D. D. Anderson and M. Zafrullah, On∗SemiHomogeneous Integral Domains, Advances in Commutative Algebra (Springer, Singapore, 2019)]. We characterize them by ∗almost superSH domains, where a domain [math] is called a ∗almost superSH domain if every nonzero proper principal ideal of [math] is a ∗product of ∗almost superhomogeneous ideals. We prove that (1) a domain [math] is a ∗almost IRKT if and only if [math] is a ∗almost superSH domain, (2) a domain is a ∗almost GKD if and only if [math] is a type 1 ∗almost superSH domain and (3) a domain [math] is a ∗almost IRKT and an AGCDdomain if and only if [math] is a ∗afgSH domain. Further, we characterize them by their integral closures. For example, we prove that a domain [math] is an almost IRKT if and only if [math] is a root extension with [math] [math]linked under [math] and [math] is an IRKT. Examples are given to illustrate the new concepts.
Citation: Journal of Algebra and Its Applications
PubDate: 20210405T07:00:00Z
DOI: 10.1142/S0219498822501365

 On maps preserving square roots of idempotent and rankone nilpotent
matrices
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Authors: Nikita Borisov, Hayden Julius, Martha Sikora
Abstract: Journal of Algebra and Its Applications, Ahead of Print.
We characterize bijective linear maps on [math] that preserve the square roots of an idempotent matrix (of any rank). Every such map can be presented as a direct sum of a map preserving involutions and a map preserving squarezero matrices. Next, we consider bijective linear maps that preserve the square roots of a rankone nilpotent matrix. These maps do not have standard forms when compared to similar linear preserver problems.
Citation: Journal of Algebra and Its Applications
PubDate: 20210331T07:00:00Z
DOI: 10.1142/S0219498822501237

 On the oriented Thompson subgroup [math] and its relatives in higher
Brown–Thompson groups
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