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An S-Topological BE-Algebras(STBE-Algebras) is a BE-Algebra equipped with a special type of topology that makes the operation (defined on it)as S-topological continuous. In this paper, we discuss the separation axioms on a STBE-Algebras. [ABSTRACT FROM AUTHOR]

This study introduces an ample Hausdorff groupoid Aˆ ⋊ R extracted from an ample Hausdorff groupoid G and a unital commutative ring R; a Hausdorff groupoid D which is the discrete twist over Aˆ ⋊ R. In the groupoid C*-algebra perspective, when R = C there is an isomorphism between the non-twisted groupoid C*-algebra (C∗(G)) and the twisted groupoid C*-algebra (C∗(Aˆ ⋊ R;D)). However, in this paper, in a purely algebraic setting, the non-twisted Steinberg algebra (AR(G)) and the twisted Steinberg algebra (AR(D;Aˆ⋊R)) are non-isomorphic. [ABSTRACT FROM AUTHOR]

In the present paper, we apply the concept of reverse derivation in rings on the concept of d - algebra to obtain the concept called a left-right (resp. right-left) reverse derivations of d-algebra X (briefly, (l, r) resp. (r, l)-reverse derivation of d-algebra), we will also, define some concepts such as regular map, composition two maps and study the related properties. Moreover, the notions of partial ordered edge d - algebra as well as d - subalgebra and their relation to our current study are obtained. In addition, some illustrative examples and counterexamples are discussed. [ABSTRACT FROM AUTHOR]

A pseudo hyper GR-algebra is an algebraic structure involving two distinct hyperoperations. Properties of this hyper algebra have been studied and given illustrations. This paper focuses on the quotient structure of pseudo hyper GR-algebras. From an equivalence relation on a pseudo hyper GR-algebra H, we can define a congruence relation on H that is used in the construction of the quotient structure H/I, where I is the congruence class of 0 under the congruence relation. Moreover, some isomorphism theorems of pseudo hyper GR-algebras are included in this paper. [ABSTRACT FROM AUTHOR]

In this paper we study the class of algebras satisfying a polynomial identity of degree six that are principal train algebras of rank 3 or 4, for which we give the explicit form of the train equation. If the rank of A is n ≥ 5 in general, we provide the form of the train equation in some cases. [ABSTRACT FROM AUTHOR]

In our paper [3] we built the functor dExt n S-1A(-; S-1B) in the category A-Alg. The purpuse of this paper is to show that if A is a ring not necessary commutative, S a central multiplicatively closed subset of A and B an (A-A)-bialgebra, then TorS-1A n (-, S-1B) : Alg-S-1A = S-1A-Modo: Ext n S-1A(-, S-1B)o is an adjunction. [ABSTRACT FROM AUTHOR]

This paper is devoted to the classification of train algebras of degree 2 and exponent 4. This classification is made in dimension at most four and according to the type of the algebra. We first show that in four dimension, the type of algebra can only be of (2, 0, 1, 1), (2, 1, 0, 1) or (2, 1, 1, 0). [ABSTRACT FROM AUTHOR]

This paper introduces the fuzzification of the dual B-algebra and presented some of its related properties. A characterization of a fuzzy (normal) dual B-algebra is also investigated. [ABSTRACT FROM AUTHOR]

The concept of the direct product of finite family of B-algebras is introduced by Lingcong and Endam[J. A. V. Lingcong and J. C. Endam, Direct product of B-algebras, Int. J. Algebra, 10(1):33-40, 2016.]. In this paper, we introduce the concept of the direct product of infinite family of B-algebras, we call the external direct product, which is a generalization of the direct product in the sense of Lingcong and Endam. Also, we introduce the concept of the weak direct product of B-algebras. Finally, we provide several fundamental theorems of (anti-)B-homomorphisms in view of the external direct product B-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we present the initiative of type 3 multi fuzzy sets which is an extension of type3 fuzzy sets. we have attempted to propose an extension of type2 multi fuzzy sets into a type3 multi fuzzy sets. In the wake of characterizing type 3 multi fuzzy sets, we examine the algebraic properties of these sets including set-theoretic operation such as complement, inclusion, union, intersection with example. Also we illustrate some algebraic properties. [ABSTRACT FROM AUTHOR]

In this paper we study an elementary use of E-infinity modules and E-infinity algebras as together they have a use in terms of describing triangulated categories. Also, we show an interpretation of E-infinity algebras where the modules are fibrant objects within the categories of differential graded co-algebras and co-modules. [ABSTRACT FROM AUTHOR]

All the results on semigroups obtained using only sets, can be written in an abstract form in a more general setting. Let us consider a recent paper to justify what we say. The biinterior ideals of semigroups introduced and studied by M. Murali Krishna Rao in Discuss. Math. Gen. Algebra Appl. in 2018, follow for more general statements about ordered semigroups. The same holds for every result of this sort on semigroups based on right (left) ideals, bi-ideals, quasiideals, interior ideals etc. for which we use sets. As a result, we have an abstract formulation of the results on semigroups obtained by sets that is in the same spirit with the abstract formulation of general topology (the so-called topology without points) initiated by Koutský, Nöbeling and, even earlier, by Chittenden, Terasaka, Nakamura, Monteiro and Ribeiro. As a consequence, results on ordered Γ-hypersemigroups and on similar simpler structures can be obtained. [ABSTRACT FROM AUTHOR]

As a system of abstract algebra, evolution algebras are commutative and non-associative algebras. There is no deep structure theorem for general non-associative algebras. However, there are deep structure theorem and classification theorem for evolution algebras because it has been introduced concepts of dynamical systems to evolution algebras. Recently, in [25], it has been studied some properties of nilpotent evolution algebra with maximal index (dim E² = dim E - 1). This paper is devoted to studying nilpotent finite-dimensional evolution algebras E with dim E² = dim E - 2. We describe Lie algebras related to the evolution of algebras. Moreover, this result allowed us to characterize all local and 2-local derivations of the considered evolution algebras. All automorphisms and local automorphisms of the nilpotent evolution algebras are found. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define a new topology called omega topology over a new structure called omega algebra and discuss some of its topological properties. Four different examples of omega topology are introduced. Furthermore, we define a new topology over a semiring in conventional algebra and we study the relationship between omega topology and weaker kinds of normality. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the concept of regular congruence relation on hyper UP- algebras and establish some homomorphism theorems on such algebras. We also examine the notion of hyper product of hyper UP-algebras. [ABSTRACT FROM AUTHOR]

This paper investigates a new class of algebra related to UP-algebras and semigroups called fully UP-semigroups (or f-UP-semigroups). It establishes some structural properties of f- UP-semigroups. It also introduces and examines f-UP-fields, f-UP-domains, f-UP-ideals, and quotient f-UP-semigroups. Moreover, it investigates the relationship between an f-UP-field and an f-UP-domain. [ABSTRACT FROM AUTHOR]

This study is based on the structure of hyper GR-algebras, an algebra that is partially related on some class of hyper BCI-algebras. This allows us to create a new structure and investigate how this two algebras are related to each other. A pseudo hyper GR-algebra involves two hyper operations and a set of axioms that come in pairs or a combination of both making it interesting like some algebras established. This paper focuses on some properties of pseudo hyper GR-algebras and its ideals. Moreover, pseudo hyper GR-ideals were defined and classified to determine their relationship to each other. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of the zero divisor graph of a hyper BCI-algebra and investigates some of its properties. [ABSTRACT FROM AUTHOR]

In this paper, using the notions of soft sets and N-structures, the notion of N-soft p-ideals in BCI-algebras is introduced, and related properties are investigated. Furthermore, relations between N-soft ideals and N-soft p-ideals are discussed. Finally, conditions for an N-soft ideal to be an N-soft p-ideal are established. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to initiate and study on the generalization of the fuzzifica tion of ideals in a class of non-associative and non-commutative algebraic structures (LA-ring). We characterize different classes of LA-ring in terms of intuitionistic fuzzy left (resp. right, bi-, generalized bi-, (1; 2)-) ideals. [ABSTRACT FROM AUTHOR]

In this paper, the notions of soft hypervector space and fuzzy soft hypervector space are introduced, and several basic properties are provided. Also, we define and analyze the concept of image and pre-image of fuzzy soft hypervector space. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the structure of pseudo-BCI algebras and get that any pseudoBCI algebra is a union of it's branches. We introduce the notion of local bounded pseudo-BCI algebras and study some related properties. Moreover we define two operations ⋀1, ⋀2 in a local bounded pseudo-BCI algebra A and two local operations ⋁1 and ⋁2 in V (a) for a ∈ M(A). We show that in a ⋀1(⋀2)-commutative local bounded pseudo-BCI algebra A, (V (a), ⋀1, ⋁1)((V (a), ⋀2, ⋁2)) forms a lattice for all a ∈ M(A). We define a Bosbach state on a local bounded pseudo-BCI algebra. Then we give two examples of local bounded pseudo-BCI algebras to show that there is local bounded pseudo-BCI algebras having a Bosbach state but there is some one having no Bosbach states. Moreover we discuss some basic properties about Bosbach states. If s is a Bosbach state of a local bounded pseudo-BCI algebra A, we prove that A/ker(s) is equivalent to an MV-algebra. We also introduce the notion of state-morphisms on local bounded pseudo-BCI algebras and discuss the relations between Bosbach states and state-morphisms. Finally we give some characterization of Bosbach states. [ABSTRACT FROM AUTHOR]

In this paper, we study (m, n)-ideals of an LA-semigroup in detail. We characterize (0,2)- ideals of an LA-semigroup S and prove that A is a (0,2)-ideal of S if and only if A is a left ideal of some left ideal of S. We also show that an LA-semigroup S is 0 - (0,2)-bisimple if and only if S is right 0-simple. Furthermore we study 0-minimal (m, n)-ideals in an LA-semigroup S and prove that if R, (L) is a 0-minimal right (left) ideal of S, then either RmLn = {0} or RmLn is a 0-minimal (m, n)-ideal of S for m, n ≥ 3. Finally we discuss (m, n)-ideals in an (m, n)-regular LA-semigroup S and show that S is (0,1)-regular if and only if L = SL where L is a (0,1)-ideal of S. [ABSTRACT FROM AUTHOR]

A soft set can be calculated by a set-valued mapping that assigns precisely one crisp subset of the universe to each parameter. In 1998, X. Liu gave Axiomatic Fuzzy set structure and El-algebra. They pointed out that ordinary fuzzy concepts or human concepts can be represented through any molecular or atomic fuzzy concepts in El-algebra over any finite set of fuzzy concepts. However, this isn't the only way to represent transitive human ideas. The definition of soft sets was extended to El-algebra in this article by taking El-algebra as universe of discourse in soft sets, and certain properties of soft El-algebras were investigated. We also introduced homomorphism between two Elalgebras. [ABSTRACT FROM AUTHOR]

We consider a series of configurations defined by fibers of a given base configuration. We prove that Markov degree of the configurations is bounded from above by the Markov complexity of the base configuration. As important examples of base configurations we consider incidence matrices of graphs and study the maximum Markov degree of configurations defined by fibers of the incidence matrices. In particular we give a proof that the Markov degree for two-way transportation polytopes is three. [ABSTRACT FROM AUTHOR]