Abstract: The left invertive law makes Abel Grassmann's groupoids (briefly AG-groupoids) a very interesting structure to study. In this paper, we define (M, N)-double-framed soft bi-ideals (briefly (M, N)-DFS bi-ideals) and (M, N)-double-framed soft generalized bi-ideals (briefly (M, N)-DFS generalized bi-ideals) of AG-groupoids and study some of its properties. We obtain some interesting results of these notions in intra-regular AG-groupoids. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: In this paper we introduce Sheffer stroke BE-algebras (briefly, SBE-algebras) and investigate a relationship between SBE-algebras and BE-algebras. By presenting a SBE-filter, an upper set and a SBE-subalgebra on a SBE-algebra, it is shown that any SBE-filter of a SBE-algebra is a SBE-subalgebra but the converse of this statement is not true. Besides we construct quotient SBE-algebras via a congruence relation defined by a special SBE-filter. We discuss SBE-homomorphisms and their properties between SBE-algebras. Finally, a relation between Sheffer stroke Hilbert algebras and SBE-algebras is established. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: In this paper, the concepts of f-prime ideals and f-semiprime ideals on a ternary semigroup are considered as a generalization of pseudo prime ideals and pseudo semiprime ideals, respectively. Then such ideals introduced are used to describe left (respectively, right) f-primary ideals on a ternary semigroup. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: As a generalization of the concept of a weakly prime ideal, we introduce the concepts of a fuzzy weak prime ideal, a fuzzy weakly 2-absorbing ideal of a lattice. Some results of fuzzy weakly 2-absorbing ideals and fuzzy weakly primary ideals are proved. We also introduce and study fuzzy weakly 2-absorbing ideals in a product of lattices. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: In this paper, we consider Leavitt path algebras having coefficients in a k-semifield. Concentrating on the aspect of k-simplicity, we find a set of necessary and sufficient conditions for the k-simplicity of the Leavitt path algebra LS(Γ) of a directed graph Γ over a non-zeroid k-semifield S. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: An involutive pocrim is a resituated integral partially ordered commutative monoid with an involution operator, consider as an algebra. In this paper it is proved that the variety of a finitely generated by involutive pocrims of finite type has a finitely based equational theory. We also study the algebraic geometry over compete lattices and we investigate the properties of being equationally Noetherian and uω-compact over such lattices. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: Let R be a commutative ring with identity. An ideal I of a ring R is called an annihilating-ideal if there exists a nonzero ideal J of R such that IJ = (0) and we use the notation 𝔸(R) for the set of all annihilating-ideals of R. In this paper, we introduce the extended annihilating-ideal graph of R, denoted by 𝔼𝔸𝔾(R). It is the simple graph with vertices 𝔸(R)* = 𝔸(R)\ {(0)}, and two distinct vertices I and J are adjacent whenever there exist two positive integers n and m such that InJm = (0) with In ≠ (0) and Jm ≠ (0). Here we discuss in detail the diameter and girth of 𝔼𝔸𝔾(R) and investigate the coincidence of 𝔼𝔸𝔾(R) with the annihilating-ideal graph 𝔸𝔾 (R). Moreover we propose open questions in this paper. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: An intuitionistic fuzzy finite state automaton assigns a membership and nonmembership values in which there is a unique membership transition on an input symbol (IFAUM) is considered. It is proved and illustrated the existence of two different intuitionistic fuzzy monoids F (𝒜) and S𝒜 from an intuitionistic fuzzy transition function of the given IFAUM 𝒜. Also it is proved that F (𝒜) and S𝒜 are anti-isomorphic as monoids. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: H. Strietz proved in 1975 that the minimum size of a generating set of the partition lattice Part(n) on the n-element set (n ≥ 4) equals 4. This classical result forms the foundation for this study. Strietz's results have been echoed by L. Zádori (1983), who gave a new elegant proof confirming the outcome. Several studies have indeed emerged henceforth concerning four-element generating sets of partition lattices. More recently more studies have presented the approach for the lower bounds on the number λ(n) of the four-element generating sets of Part(n) and statistical approach to λ(n) for small values of n. Also, G. Czédli and the present author have recently proved that certain direct products of partition lattices are also 4-generated. In a recent paper, G. Czédli has shown that this result has connection with information theory. On this basis, here we give a lower bound on the number ν(n) of 4-element generating sets of the direct product Part(n) × Part(n + 1) for n ≥ 7 using the results from previous studies. For n = 1, . . . , 5, we use a computer-aided approach; it gives exact values for n = 1, 2, 3, 4 but we need a statistical method for n = 5. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: In this paper, we introduce the concepts of n-fold obstinate ideals, n-fold normal ideals, n-fold fantastic ideals and n-fold involutive ideals in residuated lattices, state and prove some of their properties. Several characterizations of these notions are derived and the relations between those notions are investigated. Also, we construct the correspondence between the notions of n-fold ideal and n-fold filter in residuated lattices. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: In this paper, we introduce a new family of circulants GA(t, k), called Generalized Andrásfai graphs, where t, k ≥ 2 are integers. We study various parameters like diameter, girth, domination number etc. of GA(t, k). Moreover, we find the full automorphism group of GA(t, k) and compute its determining number. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: The bihyperbolic numbers are extension of hyperbolic numbers to four dimensions. In this paper we introduce and study the Fibonacci and Lucas bihypernomials, i.e., polynomials, which are a generalization of the bihyperbolic Fibonacci numbers and the bihyperbolic Lucas numbers, respectively. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: Let (G, *) be a finite group and S = {u ∈ G u ≠ u−1}, then the inverse graph is defined as a graph whose vertices coincide with G such that two distinct vertices u and v are adjacent if and only if either u * v ∈ S or v * u ∈ S. In this paper, we introduce a modified version of the inverse graph, called i*-graph associated with a group G. The i*-graph is a simple graph with vertex set consisting of elements of G and two vertices x, y ∈ Γ are adjacent if x and y are not inverses of each other. We study certain properties and characteristics of this graph. Some parameters of the i*-graph are also determined. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: In this paper, we study the structure of cyclic codes overM2(ℤ4) (the matrix ring of matrices of order 2 over ℤ4), which is perhaps the first time that the ring is considered as a code alphabet. This ring is isomorphic to ℤ4[w] + Uℤ4[w], where w is a root of the irreducible polynomial x2 + x + 1 ∈ ℤ2[x] and U≅(1111)U \cong \left({\matrix{1 & 1 \cr 1 & 1 \cr]] \right). In our work, we first discuss the structure of the ring M2(ℤ4) and then focus on the structure of cyclic codes and self-dual cyclic codes over M2(ℤ4). Thereafter, we obtain the generators of the cyclic codes and their dual codes. A few non-trivial examples are given at the end of the paper. PubDate: Thu, 20 Oct 2022 00:00:00 GMT

Abstract: We generalize the concept of a fuzzy distributive lattice by introducing the concepts of a fuzzy join-distributive pair and a fuzzy join-semidistributive pair in a fuzzy lattice. A relationship among a fuzzy join-distributive pair, a fuzzy join-semidistributive pair and a fuzzy join-modular pair is proved. It is shown that for a pair of fuzzy atoms, the notions of a fuzzy join-distributive pair and a fuzzy join-semidistributive pair coincide. PubDate: Tue, 05 Apr 2022 00:00:00 GMT

Abstract: In this work, a soft set (F, A) was introduced over a quasigroup (Q,) and the study of finite soft quasigroup was carried out, motivated by the study of algebraic structures of soft sets. By introducing the order of a finite soft quasigroup, various inequality relationships that exist between the order of a finite quasigroup, the order of its soft quasigroup and the cardinality of its set of parameters were established. By introducing the arithmetic mean 𝒜ℱ(F, A) and geometric mean 𝒢ℱ(F, A) of a finite soft quasigroup (F, A), a sort of Lagrange’s Formula (F, A) = A 𝒜ℱ(F, A) for finite soft quasigroup was gotten. Some of the inequalities gotten gave an upper bound for the order of a finite soft quasigroup in terms of the order of its quasigroup and cardinality of its set of parameters, and a lower bound for the order of the quasigroup in terms of the arithmetic mean of the finite soft quasigroup. A chain of inequalities called the Maclaurin’s inequality for any finite soft quasigroup (F, A)(Q,·) was shown to exist. A necessary and sufficient condition for a type of finite soft quasigroup to be extensible to a finite super soft quasigroup was established. This result is of practical use whenever a larger set of parameters is required. The results therein were illustrated with examples. Application to uniformity, equality and equity in distribution for social living is considered. PubDate: Tue, 05 Apr 2022 00:00:00 GMT

Abstract: The structure space of a semigroup endowed with hull kernel topology is introduced and studied. Also the structure space of a Г -semigroup is defined and a homeomorphism has been established between structure space of a Г -semigroup and the structure space of its left operator semigroup. Moreover, various properties of structure space of a Г -semigroup are studied via its left operator semigroup. PubDate: Tue, 05 Apr 2022 00:00:00 GMT

Abstract: In this paper, we transfer Davey‘s characterization for κ -Stone bounded distributive lattices to lattices with certain kinds of quotients, in particular to commutator lattices with certain properties, and obtain related results on prime, radical, complemented and compact elements, annihilators and congruences of these lattices. We then apply these results to certain congruence lattices, in particular to those of semiprime members of semi-degenerate congruence-modular varieties, and use this particular case to transfer Davey‘s Theorem to commutative unitary rings. PubDate: Tue, 05 Apr 2022 00:00:00 GMT

Abstract: In this paper, the notions of n-fold positive implicative prefilter and n-fold implicative prefilter in EQ-algebras are introduced and several properties, characterizations and equivalent conditions are provided. It is proved that the quotient EQ-algebra induced by an n-fold positive implicative prefilter is n-idempotent. Also, it is proved that in an n-idempotent EQ-algebra, any filter is an n-fold positive implicative filter. In the sequel, we investigate the relationships between these two types of prefilters. Finally, some characterizations of n-fold implicative prefilters in bounded EQ-algebras are given. PubDate: Tue, 05 Apr 2022 00:00:00 GMT

Abstract: The main purpose of this paper is to generalize the concept of linear terms. A linear term is a term in which every variable occurs at most once. K. Denecke defined partial operations on linear terms and partial clones. Moreover, their properties are also studied. In the present paper, a generalized notion of the partial clone of linear terms, which is called k-terms clone, is presented and we also study its properties. We provide a characterization of the k-terms clone being free with respect to itself. Moreover, we attempt to define mappings analogue to the concept of hypersubstitutions. PubDate: Mon, 06 Sep 2021 00:00:00 GMT