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This paper deals with applying the concept of fuzzy sets to Leibniz algebras in order to introduce and to study the descriptions of fuzzy Leibniz subalgebras and fuzzy Leibniz ideals. More concretely, our main goal is to introduce the notion of interval-valued fuzzy Leibniz ideals in Leibniz algebras. Additionally, we present some of their properties. [ABSTRACT FROM AUTHOR]

In this paper, we proved that each nonlinear non-global semi-Jordan triple higher derivable mapping on a 2-torsion free triangular algebra is an additive higher derivation. As its application, we get the similar conclusion on a nest algebra or a 2-torsion free block upper triangular matrix algebra, respectively. [ABSTRACT FROM AUTHOR]

The notion of factor set in Lie algebras is defined by Moneyhun in 1994. It was developed by Eshrati et al. on n-Lie algebras. In this paper we present an m-factor set notion on Filippov algebras and obtain some results for finite dimensional m-stem Filippov algebras. Moreover, we show that if A and B are two finite dimensional m-stem Filippov algebras or have the same dimensions, then A ∼m B if and only if A≅B. [ABSTRACT FROM AUTHOR]

In this paper, we study the geometry of an A-metric space of Subba Rao [15], by introducing the concepts of metric betweenness and its properties t1, t2, B-linearity and D-linearity. It is proved that there do not exist equilateral triangles in any Ametric space (A, A, d), where A is any representable autometrized algebra satisfying (R) and(S). It is also proved that any A-metric space is Ptolemaic. [ABSTRACT FROM AUTHOR]

Let A be a nilpotent Filippov (n-Lie) algebra of dimension d and put s(A) = (d−1n) + n − 1 − dim M (A), where M(A) denotes the multiplier of A. The aim of this paper is to classify all nilpotent n-Lie algebras A for which s(A) = 4 or 5. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the semiring of quotients of a H− semimodule semialgebra A with respect to the filter F of H−stable ideals I of A with right and left annihilators of I are zero. We establish a connection between semiring of quotients of a semialgebra A and the ring of quotients of the algebra of differences A 4. We also introduce the Hopf algebra action of the semiring of quotients and study the connection between the smash product of semialgebra of quotients and the smash product of algebra of quotients. [ABSTRACT FROM AUTHOR]

The quasi partial actions or partial actions on algebras in which some Dg's are not generated by central idempotents donot admit global actions (enveloping actions). In the process of generalizing the results of Montgomery [11, 12] and Passman [13] for such actions, we found a new class of group actions namely restricted group actions in this paper. These actions play the same role in studying quasi partial fixed rings (defined in this paper) and quasi partial skew group rings that global actions play for partial actions. [ABSTRACT FROM AUTHOR]

Given two square matrices A, B of the same size, the two matrices AB and BA may have different ranks. A non-zero square matrix A is called a rankcommutator of a family L of n × n matrices if rank(AL) = rank(LA) holds for every L in L. Let L* denote the family of all rank-commutators of L. In this paper, we investigate the members of L* for the following families L of n×n matrices: all non-zero symmetric matrices; all diagonal matrices; all diagonalizable matrices. In the process, some new notions in linear algebra are created, such as "rank-symmetric matrices" and "determinant equivalent matrices", which might be useful for other study on ranks. A few problems for further study are posed at the end of the paper. [ABSTRACT FROM AUTHOR]

The classical logics was axiomatized algebraically by means of Boolean algebras in 19th century by George Boole. Similar attempts went on 20th century for algebraic axiomatization of non-classical logics, e.g. intuitionistic logics (Brouwer and Heyting algebras), many-valued logics (Lukasiewicz, Chang's MV-algebras, Post algebras), the logic of quantum mechanics (orthomodular lattices and posets) and fuzzy logics (residuated lattices). In this paper, we are focused in a common generalization of MV-algebras and orthomodular lattices. The resulting algebras, called basic algebras, have surprisingly strong and interesting properties and they can be investigated in their own. The aim of the paper is to get an overview of results reached during the last decade. [ABSTRACT FROM AUTHOR]

Let X be a completely regular Hausdorff topological space and ∑(X) the class of all subalgebras of C(X) containing C*(X). Byun and Watson published a paper in Topology and its Application in 1991, some of whose results had been corrected in the Doctoral Dissertation of present author and reproved recently by Acharyya and Bose in a paper of Topology and its Application. In the present article we prove that the class of all prime ideals in an intermediate ring A(X) that lie between a non-maximal prime ideal and the unique maximal ideal extending it constitutes a Dedekind complete chain with atleast 2/¹ many members. A special case of this result with A(X) = C(X) (respectively C* (X)) is already covered in Gillman-Jerison text. From this it follows that if A (X) ≄ C(X) then there are atleast 2/¹ many non-maximal prime ideals in A(X). This generalizes a well known fact established by Gillman and Henriksen longtime ago and also sharpens a corresponding recent result of Acharyya and Bose. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of C*-ternary 3-Jordan derivation on the C*-ternary algebras. Then we prove that the 3-linearity and Ulam-Hyers stability of the functional equation ... in C*-ternary algebras. [ABSTRACT FROM AUTHOR]

The c-nilpotent multiplier of a Lie algebra, was introduced by Salemkar et al. Several authors investigated to develop some results on the c-nilpotent multiplier of Lie algebras. In this paper, we prove some inequalities and isomorphisms on dimension of derived algebra and the c-nilpotent multiplier of Lie algebras. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define and investigate a new equational class of algebras which we call De Morgan almost distributive lattices (or shortly De Morgan ADLs) as a common abstraction of De Morgan algebras and almost Boolean algebras (relatively complemented ADLs). [ABSTRACT FROM AUTHOR]

The notion of a state is an analogue to probability measure and it has a very important role in the theory of quantum structures. In the case of non-commutative fuzzy structures, the states were introduced by A. Dvurečenskij for pseudo-MV algebras, by G. Georgescu for pseudo-BL algebras and by A. Dvurečenskij and J. Rachůek for bounded non-commutative Rℓ-monoids. In this paper, we will investigate the existence of states on residuated lattices, pseudo-MTL algebras and pseudo-BL algebras. The main results of the paper consist of proving that any perfect pseudo-BL algebra admits a unique state-morphism, any perfect residuated lattice and any perfect pseudo-MTL algebra admits a state and there exist linear residuated lattices and linear pseudo-MTL algebras having no states. Additionally, we extend to pseudo-MTL algebras some properties of filters proved in the case of pseudo-BL algebras. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of quasi-c-principally injective modules (in short, quasi-cp-injective modules) and self-c-principally injective rings are introduced. In support of these concepts we have also provided the examples. The characterization and some properties of quasi-cp-injective modules are given in terms of their endomorphism rings. The characterization of self-c-principally injective rings is given in terms of annihilator ideals. Apart from this, the characterization of semi-simple artinian rings is given in terms of quasi-cp-injective modules. Sufficient conditions are given for quasi-cp-injective modules to become co-Hopfian and weakly co-Hopfian. In the beginning of this paper we have introduced M-c-principally injective modules for a right R-module M and have studied their properties. The examples of M-cp-injective modules are given, which are not M-principally injective modules and M-c-injective modules, respectively. [ABSTRACT FROM AUTHOR]

Automorphisms of a Weyl-type non-associative subalgebra of ̅W̅N ̅n̅m̅s were studied in [2], [3], [4], [12], [13]. There are various papers on the automorphism groups of an associative algebra, a Lie algebra, and a non-associative algebra [4], [5], [11]. It seems that there is no paper on automorphisms of a semi-Lie algebra in the literature. A degree on an algebra is used to find the derivation group of an algebra in the paper [13]. We find the automorphism groups Autonon(̅W̅N̅0, ̅0,̅12) and Autosemi-Lie (̅W̅N̅0, ̅0,̅12)[,]) of the non-associative algebra (̅W̅N̅0, ̅0,̅12) and the semi-Lie algebra (̅W̅N̅0, ̅0,̅12)[,]) respectively in this paper. The results of an algebra in this paper do not depend on its standard basis. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notions of pseudo BL-algebra of fractions and maximal pseudo BL-algebra of quotients for a pseudo BL algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek - see [13], p.36). In this paper, we prove the existence of a maximal pseudo BL-algeba of quotients for a pseudo BL-algebra (Theorem 4.7) and we give an explicit description of the pseudo BL-algebra for some classes of pseudo BL-algebras. [ABSTRACT FROM AUTHOR]

In this paper, the notion of BCC-implicative ideal, BCC-commutative ideal, BCC-positive implicative ideal. Fuzzy BCC-implicative ideal and fuzzy BCC-positive implicative ideal and the quotient BCC-algebra induced by fuzzy BCC-ideal is introduced. The following results are obtained, for a BCC-algebra X: 1) BCC-commutative (resp. positive implicative) ideal must be a BCC-ideal. 2) fuzzy BCC-commutative (resp. positive implicative)ideal must be fuzzy BCC-ideal. 3) A fuzzy set µ in a BCC-algebra X is a fuzzy BCC-commutative (resp. implicative, positive implicative) ideal of X, if and only if, for each t ∈ [1, 1], t ≤ µ(0), µt = {x ∈ X, µ(x) ≥ t} is a BCC-commutative (resp, positive implicative, implicative) ideal of X, when µt ≠ Φ, 4) Let µ is a fuzzy BCC-ideal Of BCC-algebra X, and is not a constant, define a binary relation ∼µ on X by putting X ∼micro; y if and only if µ(xy) > 0 and µ(xy) > 0, then ∼micro; is a congruence relation on X. 5) In the end of this paper we give the construction of a quotient BCC-algebra X/µ via a fuzzy BCC-ideal µ. [ABSTRACT FROM AUTHOR]

This paper deals with the way of solving inhomogeneous Cauchy-Fueter equations. An analogue of Mittag -- Leffler for regular functions of one quaternionic variable is proved in this paper, too. [ABSTRACT FROM AUTHOR]

This paper deals with the way of solving the inhomogeneous generalized Cauchy-Riemann systems in Quaternionic analysis. The Cousin problem is considered in this paper, too. [ABSTRACT FROM AUTHOR]

We define the Lie admissible non-associative algebra NAn,m,s in this paper. We show that NAn,m,s is simple. The corresponding Lie algebra of NAn,m,s is studied in the paper [4]. The matrix ring Mm(F) is a subalgebra of NAn,m,s We find all automorphisms of the algebra NA0,s,0 We define a Solid algebra by Theorem 4 in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce A-metric spaces (X, A, d), where X is a non empty set, A = (A, +, ≤, *) is a Representable Autometrized Algebra in [6], d : X × X → A is a function satisfying the formal properties of a distance function. We proved that any Ai-metric space (X, A, d) is congruent to a subdirect product of Aimetric spaces where each Ai is a totally ordered Representable autometrized algebra. [ABSTRACT FROM AUTHOR]

In this paper we study p-ideals and p-filters of a p-algebra. We give a Stone based separation theorem for p-ideals. We also give some characterizations of p-ideals and p-filters. We show that both the set of all p-ideals and the set of all p-filters of a p-algebra form a distributive p-algebra. Finally, we prove that the two p-algebras are isomorphic. [ABSTRACT FROM AUTHOR]

The quantum matrix algebra Mq(2) can be constructed through Ore extension. This is used to construct Mq(2)-modules from modules over its subalgebra. In this paper, we illustrate this approach and for a particular module over the subalgebra we determine all submodules of the induced Mq(2)-module for either q being a root of unity or not. [ABSTRACT FROM AUTHOR]

In this paper, we identify the (0, *)-ideals of a demi-pseudocomplemented MS-algebra L as the kernel of the boolean congruences on L. In particular, we show that these ideals are precisely the kernels of the congruences # on L such that (L/v; *) is boolean, and that they form a sublattice of the lattice of ideals of L that is isomorphic to the interval [G, ι] of the congruence lattice of L where G is the Glivenko congruence and ι is the universal congruence. [ABSTRACT FROM AUTHOR]

In this paper, we define a Quasi Heyting ADL and derive some necessary and sufficient conditions for an SHADL to become a Quasi Heyting ADL.We also define the concept of an Almost Semi Heyting Algebra and derive some equivalent conditions for an ADL (L,⋁,⋀, 0) with a binary operation → and a maximal element m, to become an Almost Semi Heyting Algebra. [ABSTRACT FROM AUTHOR]

In this paper, a relation between number of convex sublattices ∣CS(L)∣ and number of incomparable pairs n(L) of a finite lattice L is obtained. For a Boolean algebra Bk of k atoms, it is proved that (a) ∣CS(Bk)∣ = 3k and (b) n(Bk) = 2k-1(2k + 1) - 3k. Further, several tight lower and upper bounds for ∣CS(L)∣ in terms of number of join-irreducibles of L are given. [ABSTRACT FROM AUTHOR]

In this paper, the concept of essentially critically compressible modules are introduced, and related properties are investigated. The concept of essentially critically compressible modules are generalization of critically compressible modules discussed by Zelmanowitz. We have also provided some characterization of critically compressible modules in terms of CS modules, nonsingular modules, continuous modules and cyclic modules. [ABSTRACT FROM AUTHOR]

In this paper we discuss p-algebras and some of their subclasses. A notion of DM-algebras is introduced which is an important subclass of p-algebras. We give some characterizations of subclasses of p-algebras. We also give some characterizations of p-ideals of a p-algebra. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of Zinbiel n-algebra and study some of its properties. Also, we explain the relation between Leibniz n-algebras and Zinbiel n-algebras. Finally, we classify some nilpotent Zinbiel n-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an MS-algebra with double demi- pseudocomplementation, denoted by ddpMS. In particular, we show that there are precisely thirty six non-isomorphic subdirectly irreducible ddpMS-algebras via Priestley duality. [ABSTRACT FROM AUTHOR]

.Puczylowski established the general theory of radicals of the objects called algebras, Zongwen Yang, Zhuyuan Yang and Jiangmin Pan had established the ideals product axioms and the axioms system of normal classes of product algebras and given the general radical theory and some properties of the supernilpotent radicals, the special radicals and the Bear radical in normal classes of product algebras. In this paper, we give the properties of semihereditary radical, semisupernilpotent radicals, weakly semispecial class of algebras, weakly supernilpotent radical, simplehereditary radical, simplehereditary weakly supernilpotent radical, semispecial class of algebras, semispecial radicals and the structure of semisupernilpotent radicals, simplehereditary weakly supernilpotent radical, semispecial radicals in normal classes of product algebras. [ABSTRACT FROM AUTHOR]

In this paper we give some characterizations for idempotent-separating congruences on E-inversive semigroups whose idempotents form a rectangular band. We also give some characterizations for this kind of congruences on E*-dense semigroups whose idempotents form a *-rectangular band, which are analogous to parts for E-inversive semigroups. [ABSTRACT FROM AUTHOR]

In this paper characterization for non-symmetric skew lattices, with number of elements less than or equal to ten, is obtained. Non-Symmetric skew lattices with least number of elements are described, which are at the same time the examples to show that the converse of the Spink's theorem ([1, Corollary 4]) however is not true. [ABSTRACT FROM AUTHOR]

In this paper we establish a criterion on the structure constants of a composition algebra C over Δ(x) to admit an extension of the non-archimedean valuation vp on Δ(x). [ABSTRACT FROM AUTHOR]

The pseudoachromatic number of a graph G is the maximum size of a vertex partition of G (where the sets of the partition may or may not be independent) such that there is at least one edge of G between any two distinct parts. In this paper, the pseudoachromatic number is determined for some graphs. [ABSTRACT FROM AUTHOR]

The Signed Brauer algebras Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. which are homomorphic images of the subgroups Ot(m) of orthogonal groups contain the Brauer algebras Bn (x) and the group algebras Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., where Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. is the wreath product of ℤ2 by Sn. In this paper a complete set of inequivalent irreducible Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. - modules is constructed and used to understand a cellular structure of Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.. [ABSTRACT FROM AUTHOR]

In this paper we discuss some special generalizations of equationally Noetherian property which naturally arise in the universal algebraic geometry. We introduce weakly equationally Noetherian, qω-compact, uω-compact, and weakly uω-compact algebras and then examine properties of such algebras. Also we consider the connections between five classes: the class of equationally Noetherian algebras, the class of weakly equationally Noetherian algebras, the class of uω-compact algebras, the class of weakly uω-compact algebras, and the class of qω-compact algebras. [ABSTRACT FROM AUTHOR]

In this paper, we give a Gröbner-Shirshov basis of the free dendriform algebra as a quotient algebra of an L-algebra. As applications, we obtain a normal form of the free dendriform algebra. Moreover, Hilbert series and Gelfand-Kirillov dimension of finitely generated free dendriform algebras are obtained. [ABSTRACT FROM AUTHOR]

In this paper, by using the generating sequence and relations given by Ringel for his Ringel-Hall algebra in [9], we give a Gröbner-Shirshov basis for quantum group of type B2. [ABSTRACT FROM AUTHOR]

Number-Theoretic properties are used to classify simple graphs that are finite with no isolated vertices. A graph G of size q is defined to be a product (0, 1) vertex magic if there is a labeling from E(G) onto {1,..., q} such that at each vertex v, the product of the labels on the edges incident with v is the same. Similarly a graph G with p vertices and q edges is defined to be (1, 1) product edge-magic if there is a labeling 푓 from V(G) ∪ E(G) onto {1,...,p + q} with the property that 푓(u) ⋅ 푓(v) ⋅ 푓 (uv) = κ is a constant where κ is called the common edge count for any edge uv of G. Bertrand's postulate can be used to completely characterize product (0, 1) magic graphs and product (1, 1) edge-magic graphs without isolated vertices. In this paper we prove that a graph G of size q is product (0, 1) vertex magic if and only if q ≤ 1 and a graph of size q without isolated vertices is product (1, 1) edge magic if and only if q ≤ 1. [ABSTRACT FROM AUTHOR]

Let S = {x1, ..., xn} be a set of n distinct positive integers and a ≥ 1 an integer. The matrix having the a-th power (xi, xj)a of the greatest common divisor of xi and xj as its I, j-entry is called a-th power greatest common divisor (GCD) matrix defined on S, denoted by (Sa). Similarly we can define the a-th power LCM matrix [Sa]. In this paper, we show that if a, b are positive integers and a ...b, then for S = {1, x, ..., xn-1}, where x > 1 is any positive integer, we have det(Sa) ...det(Sb), det[Sa] ...det[Sb] and det(Sa) ...det[Sb]. This confirms partially a conjecture recently proposed by Hong. [ABSTRACT FROM AUTHOR]

We observe that a lobster with diameter at least five has a unique path H = x1, x2, . . . , xm with the property that, besides the adjacency in H, both x1 and xm are adjacent to the centers of at least one K1,s, where s > 0, and each xi, 2 ≤ i ≤ m-1, is at most adjacent to the centers of some K1,s, where s ≥ 0. This unique path H is called the central path of the lobster. We call K1,s an even branch if s is nonzero even, an odd branch if s is odd, and a pendant branch if s = 0. In this paper, we develop methods to get interlaced and graceful lobsters by joining smaller lobsters satisfying certain conditions. The interlaced and graceful lobsters we obtain here may have distinct features than those exist in literature [2], [5], [6], [7], [8], [9], and [11] that (i) some vertices on the central path need not be attached to any non-pendant branch and (ii) some vertices on the central path may have degree odd. We also prove that all diameter four trees other than the caterpillars are not interlaced. [ABSTRACT FROM AUTHOR]

Yamada first described the semidirect product structure of left (right, quasi-) inverse semigroups in 1973. Later, Sen, Ghost and Pal gave the structure and characteristics of LR-regular orthogroups. The subdirect product and dually-semidirect structure of LR-inverse semigroups were further given by Du and Guo. In this paper, we consider the subdirect product of the so-called WLR-inverse semigroups. This kind of semigroups forms a common generalization of left (right) inverses, LR-inverse semigroups and LR-regular orthogroups. [ABSTRACT FROM AUTHOR]

Let H be a normal subgroup of a group G and MH(G) = {M| M < ·G and H ≰ Mg: In this paper, we investigate the properties of θ-pairs by using the set MH(G). Several new conditions which imply G to be solvable are obtained. Some results given in [4] are also improved. [ABSTRACT FROM AUTHOR]

In this paper, we define β-insulator and strongly prime Γ-rings. We also prove that the following main results: (i) If a Γ-ring M is weakly semiprime then M is strongly prime if and only if its left operator ring L is right strongly prime and its right operator ring R is left strongly prime. (ii) If M is strongly prime Γ-ring,then their left and right operator rings are Morita equivalent. [ABSTRACT FROM AUTHOR]

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the corresponding graph algebra A(G)̲ satisfies s ≈ t. A graph G = (V;E) is called a right self-distributive graph if the graph algebra A(G)̲ satisfies the equation ((xy)z) ≈ ((xz)(yz)). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring in s and t are replaced by any term operations of A̲ of the appropriate arity, the resulting identities hold in A̲. In this paper, we characterize right self-distributive graph algebras, identities and hyperidentities in right self-distributive graph algebras. [ABSTRACT FROM AUTHOR]

In this paper, we investigate regular injectivity of S-posets over Clifford pomonoids equipped with the natural partial order. Several characterization theorems of regular self-injectivity of such Clifford pomonoids, are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we determine those subvarieties in the class of symmetric extended de Morgan algebras that have the amalgamation property. [ABSTRACT FROM AUTHOR]

In this paper, we give the characterizations of monoids over which all right Rees factor acts of S satisfying condition (PWP)(or (WP)) have some properties that follow from projectivity. We also consider the characterizations of monoids over which all right Rees factor acts of S having some flatness properties satisfy condition (PWP)(or (WP)). [ABSTRACT FROM AUTHOR]