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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]

The influx of researches on hyperstructure theory has encouraged many researchers to introduce new algebras. Notable among these is the work of Indangan and Petalcorin who introduced hyper GR-algebra and that of Macodi and Petalcorin who studied fuzzification of hyper GR-algebra. Macodi extended the fuzzification of hyper GR-algebra into intuitionistic fuzzification and introduced the concept of an intuitionistic fuzzy hyper GR-ideal. Following the works of Macodi and Petalcorin, this paper established an intuitionistic fuzzy implicative hyper GR-ideal and obtained its characterization using level subsets. Moreover, some properties of intuitionistic fuzzy implicative hyper GR-ideals are presented. [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]

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]

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]

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, 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]

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]

In this paper we try to find the finiteness conditions for union of two finite semigroups with a specially defined binary equation. Moreover we find the ranks of the semigroup B(G, n). [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study new classes of sets called ρ-closed sets and ρs -closed sets, ρ-open sets and ρs -open sets. Moreover, we present two new types of continuities called ρ- continuity and ρs-continuity and investigate some of their fundamental properties. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a quantum space generated by three noncommutative coordinates with two commutation parameters. We also give a Hopf algebra structure in order to construct a bicovariant differential calculus over this quantum space. Morever, it is shown that noncommutative derivative operators corresponding to the coordinates comprise a Weyl algebra deformed by the commutation parameters. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to give a new generalization of the operator-valued Poisson kernel and discuss its some applications. [ABSTRACT FROM AUTHOR]

In this paper we introduce a stronger type of primary decomposition of a Noetherian ring. We call such a ring a Transparent ring and show that if R is a commutative Noetherian ring, which is also an algebra over Q (the field of rational numbers); σ an automorphism of R and δ a σ-derivation of R such that δ(σ(a)) = σ(δ(a)), for all a ϵ R. Further more if aσ(a) ϵ P(R) implies that a ϵ P(R), (P(R) the prime radical of R), then R[χ;σ,δ] is a Transparent ring. [ABSTRACT FROM AUTHOR]

In this paper, Numerical solution of Partial Diferential-Algebraic Equa- tions(PDAEs) is considered by Multivariate Padè Approximations. We applied these method to one example. First Partial Diferential-Algebraic Equation(PDAE) has been converted to power series by two-dimensional diferential transformation,Then the numerical solution of equation was put into Multivariate Padè series form. Thus we obtained numerical solution of Partial Diferential-Algebraic Equa- tion(PDAE). [ABSTRACT FROM AUTHOR]

Let G = (V, E) be a given connected simple (p, q)-graph, and an arbitrary nonempty subset M ⊆ V(G) of G and for each v ∈ V(G), define NM j [u] = {v ∈ M : d(u, v) = j}. Clearly, then Nj[u] = NV(G) j [u]. B.D. Acharya [2] defined the M-eccentricity of u as the largest integer for which NM j [u] ≠ϑ; and the p ×(dG +1) nonnegative integer matrix DM G = (NM j [vi]), called the M-distance neighborhood pattern (or, M-dnp) matrix of G. The matrix D*M G is obtained from DM G by replacing each nonzero entry by 1. Clearly, fM(u) = { j : NM j [u] ≠ϑ;}. Hence, in particular, if fM : u → fM(u) is an injective function, then the set M is a distance-pattern distinguishing set (or, a 'DPD-set' in short) of G and G is a dpd-graph. If fM(u) - {0} is independent of the choice of u in G then M is an open distance-pattern uniform (or, ODPU) set of G. A study of these sets is expected to be useful in a number of areas of practical importance such as facility location [5] and design of indices of "quantitative structureactivity relationships" (QSAR) in chemistry [3, 10]. This paper is a study of M-dnp matrices of a dpd-graph. [ABSTRACT FROM AUTHOR]

If P and Q are two idempotents on a Hilbert space, in this paper, we prove that Fredholmness of aP + bQ - cPQ is independent of the choice of a, b, c with ab ≠ 0 [ABSTRACT FROM AUTHOR]

In this paper we defined the double infinite matrix A = a(m, n, k)and study the action of A on f ? L²(R) and on its prolate spheroidal wavelet coefficients. We also find the frame condition for A-transform of f ? L²(R) whose wavelet series expansion is known. 2000 Mathematics Subject Classifications: 42C15,41A17,42C40 [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to derive some inclusion properties and argument estimates of certain normalized analytic functions in the open unit disk, which are defined by means of a class of multiplier transformations. Furthermore, the integral preserving properties in a sector are investigated for these multiplier transformations. [ABSTRACT FROM AUTHOR]

Pepin's test provides a necessary and sufficient condition for a Fermat number to be prime. The Lucas-Lehmer test does similarly for a Mersenne number. These tests share a common nature. However, this is evident neither by their usual statements nor their usual treatment in the literature. Furthermore, it is unusual to even find a proof of the latter result in elementary textbooks. The intent of this paper is to bring to light the equivalent structure of these two primality tests [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]

The generic identification problem is to decide whether a stochastic process (Xt) is a hidden Markov process and if yes to infer its parameters for all but a subset of parametrizations that form a lower-dimensional subvariety in parameter space. Partial answers so far available depend on extra assumptions on the processes, which are usually centered around stationarity. Here we present a general solution for binary-valued hidden Markov processes. Our approach is rooted in algebraic statistics hence it is geometric in nature. We find that the algebraic varieties associated with the probability distributions of binary-valued hidden Markov processes are zero sets of determinantal equations which draws a connection to well-studied objects from algebra. As a consequence, our solution allows for algorithmic implementation based on elementary (linear) algebraic routines. [ABSTRACT FROM AUTHOR]

The article presents the insights of various guest editors regarding the "Journal of Algebraic Statistics" (JAlgStat). According to Hari M. Srivastava, JAlgStat will be heartily welcomed by the mathematical and statistical communities. Arjun K. Gupta also says that the journal will bond researchers who work on problems in the field of Algebraic Statistics. Ruriko Yoshida describes Algebraic Statistics as an exciting field that is why he wishes success for JAlgStat.

The article presents the authors' insights regarding algebraic statistics. The authors say that algebraic statistics is an active discipline that focuses on algebraic geometry applications and its computational tools in the models of statistics. The authors mention the example applications of algebraic statistics, including operations research, mathematical modeling, and model identification. Meanwhile, submissions for the "Journal of Algebraic Statistics" (JAlgStat) are being sought.