Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 39)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 3)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 5)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 20)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 9)
Advances in Materials Science     Open Access   (Followers: 19)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 19)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 8)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 6)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 2)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 3)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 1)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 13)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 8)
American Journal of Operations Research     Open Access   (Followers: 6)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 9)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 14)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 4)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access   (Followers: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 11)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 2)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 21)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 7)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 17)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 1)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 2)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 4)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 2)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 18)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 9)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 11)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 33)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Eco Matemático     Open Access  
Econometrics     Open Access   (Followers: 2)

        1 2 3 4 | Last

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Algebra Universalis
Journal Prestige (SJR): 0.583
Citation Impact (citeScore): 1
Number of Followers: 2  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1420-8911 - ISSN (Online) 0002-5240
Published by Springer-Verlag Homepage  [2469 journals]
  • Mal’tsev products of varieties, II

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      Abstract: Abstract The Mal’tsev product of two varieties of the same similarity type is not in general a variety, because it can fail to be closed under homomorphic images. In the previous paper we provided new sufficient conditions for such a product to be a variety. In this paper we extend that result by weakening the assumptions regarding the two varieties. We also explore the various special cases of our new result and provide a number of examples of its application.
      PubDate: 2022-05-21
       
  • Free-lattice functors weakly preserve epi-pullbacks

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      Abstract: Abstract Suppose p(x, y, z) and q(x, y, z) are terms. If there is a common “ancestor” term \(s(z_{1},z_{2},z_{3},z_{4})\) specializing to p and q through identifying some variables $$\begin{aligned} p(x,y,z)&\approx s(x,y,z,z)\\ q(x,y,z)&\approx s(x,x,y,z), \end{aligned}$$ then the equation $$\begin{aligned} p(x,x,z)\approx q(x,z,z) \end{aligned}$$ is a trivial consequence. In this note we show that for lattice terms, and more generally for terms of lattice-ordered algebras, a converse is true, too. Given terms p, q,  and an equation where \(\{u_{1},\ldots ,u_{m}\}=\{v_{1},\ldots ,v_{n}\},\) there is always an “ancestor term” \(s(z_{1},\ldots ,z_{r})\) such that \(p(x_{1},\ldots ,x_{m})\) and \(q(y_{1},\ldots ,y_{n})\) arise as substitution instances of s,  whose unification results in the original equation ( \(*\) ). In category theoretic terms the above proposition, when restricted to lattices, has a much more concise formulation:Free-lattice functors weakly preserve pullbacks of epis. Finally, we show that weak preservation is all that we can hope for. We prove that for an arbitrary idempotent variety \({{\mathcal {V}}}\) the free-algebra functor \(F_{{\mathcal {V}}}\) will not preserve pullbacks of epis unless \({{\mathcal {V}}}\) is trivial (satisfying \(x\approx y\) ) or \({{\mathcal {V}}}\) contains the “variety of sets” (where all operations are implemented as projections).
      PubDate: 2022-04-23
       
  • Varieties with existentially definable factor congruences

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      Abstract: Abstract We study the varieties with \(\vec {0}\) and \(\vec {1}\) where factor congruences are definable by existential formulas parameterized by central elements. This continues previous work on equational definability of factor congruences.
      PubDate: 2022-04-22
       
  • Nuclear ranges in implicative semilattices

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      Abstract: Abstract A nucleus on a meet-semilattice A is a closure operation that preserves binary meets. The nuclei form a semilattice \(\mathrm{N }A\) that is isomorphic to the system \({\mathcal {N}}A\) of all nuclear ranges, ordered by dual inclusion. The nuclear ranges are those closure ranges which are total subalgebras (l-ideals). Nuclei have been studied intensively in the case of complete Heyting algebras. We extend, as far as possible, results on nuclei and their ranges to the non-complete setting of implicative semilattices (whose unary meet translations have adjoints). A central tool are so-called r-morphisms, that is, residuated semilattice homomorphisms, and their adjoints, the l-morphisms. Such morphisms transport nuclear ranges and preserve implicativity. Certain completeness properties are necessary and sufficient for the existence of a least nucleus above a prenucleus or of a greatest nucleus below a weak nucleus. As in pointfree topology, of great importance for structural investigations are three specific kinds of l-ideals, called basic open, boolean and basic closed.
      PubDate: 2022-04-12
       
  • Characterizing the commutator in varieties with a difference term

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      Abstract: Abstract We extend the validity of Kiss’s characterization of “ \([\alpha ,\beta ]=0\) ” from congruence modular varieties to varieties with a difference term. This fixes a recently discovered gap in our paper Kearnes et al. (Trans Am Math Soc 368:2115–2143, 2016). We also prove some related properties of Kiss terms in varieties with a difference term.
      PubDate: 2022-04-06
       
  • Acts with identities in the congruence lattice

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      Abstract: Abstract We prove that for any act X over a finite semigroup S, the congruence lattice \({{\,\mathrm{Con}\,}}X\) embeds the lattice \({{\,\mathrm{Eq}\,}}M\) of all equivalences of an infinite set M if and only if X is infinite. Equivalently: for an act X over a finite semigroup S, the lattice \({{\,\mathrm{Con}\,}}X\) satisfies a non-trivial identity if and only if X is finite. Similar statements are proved for an act with zero over a completely 0-simple semigroup \({\mathcal {M}}^0(G,I,\Lambda ,P)\) where \( G , I <\infty \) . We construct examples that show that the assumption \( G , I <\infty \) is essential.
      PubDate: 2022-04-05
       
  • An algebraic theory of clones

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      Abstract: Abstract We introduce the notion of clone algebra ( \(\mathsf {CA}\) ), intended to found a one-sorted, purely algebraic theory of clones. \(\mathsf {CA}\) s are defined by identities and thus form a variety in the sense of universal algebra. The most natural \(\mathsf {CA}\) s, the ones the axioms are intended to characterise, are algebras of functions, called functional clone algebras ( \(\mathsf {FCA}\) ). The universe of a \(\mathsf {FCA}\) , called \(\omega \) -clone, is a set of infinitary operations on a given set, containing the projections and closed under finitary compositions. The main result of this paper is the general representation theorem, where it is shown that every \(\mathsf {CA}\) is isomorphic to a \(\mathsf {FCA}\) and that the variety \(\mathsf {CA}\) is generated by the class of finite-dimensional \(\mathsf {CA}\) s. This implies that every \(\omega \) -clone is algebraically generated by a suitable family of clones by using direct products, subalgebras and homomorphic images. We conclude the paper with two applications. In the first one, we use clone algebras to give an answer to a classical question about the lattices of equational theories. The second application is to the study of the category of all varieties of algebras.
      PubDate: 2022-03-20
       
  • Some partial results on the cancellation law for the tensor product of
           complete lattices

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      Abstract: Abstract In this paper we study the cancellation law for the tensor product in the category \(\mathsf {Sup}\) of complete lattices and join-preserving maps. First, we investigate the tensor product of generalized power-set lattices. Based on which, we prove that the cancellation law for the tensor product has a close relation to that for the cartesian product of posets, and give a class of complete lattices which do not satisfy the cancellation law for the tensor product. Then, we also investigate the cancellation law for particular subclasses of complete lattices.
      PubDate: 2022-03-20
       
  • Canonical extensions of lattices are more than perfect

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      Abstract: Abstract In a paper published in 2015, we introduced TiRS graphs and TiRS frames to create a new natural setting for duals of canonical extensions of lattices. Here, we firstly introduce morphisms of TiRS structures and put our correspondence between TiRS graphs and TiRS frames into a full categorical framework. We then answer Problem 2 from our 2015 paper by characterising the perfect lattices that are dual to TiRS frames (and hence TiRS graphs). We introduce a new subclass of perfect lattices called PTi lattices and show that the canonical extensions of lattices are PTi lattices, and so are ‘more’ than just perfect lattices. We illustrate the correspondences between classes of our newly-described PTi lattices and classes of TiRS graphs by examples. We conclude by outlining a direction for future research.
      PubDate: 2022-03-19
       
  • Adjoint maps between implicative semilattices and continuity of localic
           maps

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      Abstract: We study residuated homomorphisms (r-morphisms) and their adjoints, the so-called localizations (or l-morphisms), between implicative semilattices, because these objects may be characterized as semilattices whose unary meet operations have adjoints. Since left resp. right adjoint maps are the residuated resp. residual maps (having the property that preimages of principal downsets resp. upsets are again such), one may not only regard the l-morphisms as abstract continuous maps in a pointfree framework (as familiar in the complete case), but also characterize them by concrete closure-theoretical continuity properties. These concepts apply to locales (frames, complete Heyting lattices) and provide generalizations of continuous and open maps between spaces to an algebraic (not necessarily complete) pointfree setting.
      PubDate: 2022-03-19
       
  • Saturated free algebras and almost indiscernible theories

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      Abstract: Abstract We extend the concept of “almost indiscernible theory” introduced by Pillay and Sklinos in 2015 (which was itself a modernization and expansion of Baldwin and Shelah from 1983), to uncountable languages and uncountable parameter sequences. Roughly speaking a theory \(T\) is almost indiscernible if some saturated model is in the algebraic closure of an indiscernible set of sequences. We show that such a theory \(T\) is nonmultidimensional, superstable, and stable in all cardinals \(\ge T \) . We prove a structure theorem for sufficiently large \( a \) -models \(M\) , which states that over a suitable base, \(M\) is in the algebraic closure of an independent set of realizations of weight one types (in possibly infinitely many variables). We also explore further the saturated free algebras of Baldwin and Shelah in both the countable and uncountable context. We study in particular theories and varieties of \(R\) -modules, characterizing those rings \( R \) for which the free \( R \) -module on \( \left R\right ^{+} \) generators is saturated, and pointing out a counterexample to a conjecture by Pillay and Sklinos.
      PubDate: 2022-02-01
      DOI: 10.1007/s00012-021-00766-x
       
  • Right-cancellable protomodular algebras

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      Abstract: Abstract A new protomodular analog of the classical criterion for the existence of a group term in the algebraic theory of a variety of universal algebras is given. To this end, the notion of a right-cancellable protomodular algebra is introduced. The translation group functor from the category of right-cancellable algebras of a protomodular variety to the category of groups is constructed. It is proved that the algebraic theory of a variety of universal algebras contains a group term if and only if it contains protomodular terms with respect to which all algebras from the variety are right-cancellable. Moreover, the right-cancellable algebras from the simplest protomodular varieties are characterized as sets with principal group actions as well as groups with simple additional structures.
      PubDate: 2022-01-29
      DOI: 10.1007/s00012-021-00747-0
       
  • Riesz and pre-Riesz monoids

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      Abstract: Abstract Call a directed partially ordered cancellative divisibility monoid M a Riesz monoid if for all \(x,y_{1},y_{2}\ge 0\) in M,  \(x\le y_{1}+y_{2}\Rightarrow x=x_{1}+x_{2}\) where \(0\le x_{i}\le y_{i}\) . We explore the necessary and sufficient conditions under which a Riesz monoid M with \(M^{+}=\{x\ge 0\mid x\in M\}=M\) generates a Riesz group and indicate some applications. We call a directed p.o. monoid M \(\Pi \) -pre-Riesz if \( M^{+}=M\) and for all \(x_{1},x_{2}, \dots ,x_{n}\in M\) , \({{\,\mathrm{glb}\,}}(x_{1},x_{2},\dots ,x_{n})=0\) or there is \(r\in \Pi \) such that \(0<r\le x_{1},x_{2},\dots ,x_{n},\) for some subset \(\Pi \) of M. We explore examples of \(\Pi \) -pre-Riesz monoids of \(*\) -ideals of different types. We show for instance that if M is the monoid of nonzero (integral) ideals of a Noetherian domain D and \(\Pi \) the set of invertible ideals, M is \(\Pi \) -pre-Riesz if and only D is a Dedekind domain. We also study factorization in pre-Riesz monoids of a certain type and link it with factorization theory of ideals in an integral domain.
      PubDate: 2022-01-16
      DOI: 10.1007/s00012-021-00765-y
       
  • Abstractly constructed prime spectra

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      Abstract: The main purpose of this paper is a wide generalization of one of the results abstract algebraic geometry begins with, namely of the fact that the prime spectrum \({\mathrm {Spec}}(R)\) of a unital commutative ring R is always a spectral (= coherent) topological space. In this generalization, which includes several other known ones, the role of ideals of R is played by elements of an abstract complete lattice L equipped with a binary multiplication with \(xy\leqslant x\wedge y\) for all \(x,y\in L\) . In fact when no further conditions on L are required, the resulting space can be and is only shown to be sober, and we discuss further conditions sufficient to make it spectral. This discussion involves establishing various comparison theorems on so-called prime, radical, solvable, and locally solvable elements of L; we also make short additional remarks on semiprime elements. We consider categorical and universal-algebraic applications involving general theory of commutators, and an application to ideals in what we call the commutative world. The cases of groups and of non-commutative rings are briefly considered separately.
      PubDate: 2022-01-16
      DOI: 10.1007/s00012-021-00764-z
       
  • Mitschke’s theorem is sharp

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      Abstract: Abstract Mitschke showed that a variety with an m-ary near-unanimity term has Jónsson terms \(t_0, \dots , t _{2m-4} \) witnessing congruence distributivity. We show that Mitschke’s result is sharp. We also evaluate the best possible number of Day terms witnessing congruence modularity. More generally, we characterize exactly the best bounds for many congruence identities satisfied by varieties with an m-ary near-unanimity term. Finally we present some simple observations about terms with just one “dissenter”, a generalization of a minority term.
      PubDate: 2022-01-12
      DOI: 10.1007/s00012-021-00762-1
       
  • The least left n-trinilpotent congruence on the free trioid

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      Abstract: Abstract In the author’s recent paper, the free left (right) n-trinilpotent trioid was constructed. Our aim is to characterize the least left (right) n-trinilpotent congruence on the free trioid.
      PubDate: 2021-12-31
      DOI: 10.1007/s00012-021-00758-x
       
  • On the complexity of equational decision problems for finite height
           complemented and orthocomplemented modular lattices

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      Abstract: Abstract We study the computational complexity of the satisfiability problem and the complement of the equivalence problem for complemented (orthocomplemented) modular lattices L and classes thereof. Concerning a simple L of finite height, \(\mathcal {NP}\) -hardness is shown for both problems. Moreover, both problems are shown to be polynomial-time equivalent to the same feasibility problem over the division ring D whenever L is the subspace lattice of a D-vector space of finite dimension at least 3. Considering the class of all finite dimensional Hilbert spaces, the equivalence problem for the class of subspace ortholattices is shown to be polynomial-time equivalent to that for the class of endomorphism \(*\) -rings with pseudo-inversion; moreover, we derive completeness for the complement of the Boolean part of the nondeterministic Blum-Shub-Smale model of real computation without constants. This result extends to the additive category of finite dimensional Hilbert spaces, enriched by adjunction and pseudo-inversion.
      PubDate: 2021-12-31
      DOI: 10.1007/s00012-021-00760-3
       
  • On fraction-dense algebraic frames

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      Abstract: We abstract the notion of fraction-density of f-rings (introduced by Anthony Hager and Jorge Martínez) to algebraic frames. We say an algebraic frame with the finite intersection property on compact elements is fraction-dense if each of its polars is a polar of a compact element. This turns out to be a “conservative” extension of the fraction-density property in the sense that a reduced f-ring is fraction-dense precisely when its frame of radical ideals is fraction-dense. We characterize these frames and study properties of some other types of algebraic frames that arise naturally in the characterizations of the fraction-dense ones.
      PubDate: 2021-12-31
      DOI: 10.1007/s00012-021-00763-0
       
  • Lattices with normal elements

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      Abstract: Abstract By several postulates we introduce a new class of algebraic lattices, in which a main role is played by so called normal elements. A model of these lattices are weak-congruence lattices of groups, so that normal elements correspond to normal subgroups of subgroups. We prove that in this framework many basic structural properties of groups turn out to be lattice-theoretic. Consequently, we give necessary and sufficient conditions under which a group is Hamiltonian, Dedekind, abelian, solvable, supersolvable, metabelian, finite nilpotent. These conditions are given as lattice-theoretic properties of a lattice with normal elements.
      PubDate: 2021-11-29
      DOI: 10.1007/s00012-021-00759-w
       
  • Free products of digroups

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      Abstract: Abstract We construct the free products of arbitrary digroups, and thus we solve an open problem of Zhuchok.
      PubDate: 2021-11-29
      DOI: 10.1007/s00012-021-00761-2
       
 
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