Showing papers in "International Journal of Algebra in 2013"
TL;DR: In this paper, the authors constructed some new difference sequence spaces defined by a sequence of modulus functions and studied some topological and algebraic properties of these spaces, including topological properties of the modulus function.
Abstract: In this paper, we have constructed some new difference sequence spaces defined by a sequence of modulus functions and study some topological and algebraic properties of these spaces.
14 citations
TL;DR: The characterization of the group of units of any commutative ring has not been done in general, and previous studies have restricted the classes of rings or groups under consideration.
Abstract: The characterization of the group of units of any commutative ring has not been done in general, and previous studies have restricted the classes of rings or groups under consideration. In this work, we determine the structures of the groups of units of commutative completely primary finite rings R of characteristic p n for some prime integer p and positive integer n.
13 citations
TL;DR: In this article, various properties of multiplicative ideals in a graded ring are discussed and the set of P -primary ideals and modules of R when P is a graded multiplication prime ideal and modules.
Abstract: Let G be a multiplicative group and R be a G -graded commutative ring and M a G -graded R -module. Various properties of multiplicative ideals in a graded ring are discussed and we extend this to graded modules over graded rings. We have also discussed the set of P -primary ideals and modules of R when P is a graded multiplication prime ideals and modules.
13 citations
TL;DR: In this paper, it was shown that a ring R is finite if and only if clique number of the graph G (associated with R as above) is finite, which turns out to be the maximum of the cardinalities of all maximal ideals in R.
Abstract: Let R be a commutative ring with identity. Let G be a graph with vertices as elements of R, where two distinct vertices a and b are adjacent if and only if there is a maximal ideal of R containing both. In this paper we show that a ring R is finite if and only if clique number of the graph G (associated with R as above) is finite. We also have shown that for a semilocal ring R, the chromatic number of the graph G is equals to the clique number of G which turns out to be the maximum of the cardinalities of all the maximal ideals in R. Mathematics Subject Classification: Primary 13C99, Secondary 05C99, 13M99
13 citations
TL;DR: The parameters of the minimal cyclic codes of length 22 are discussed and the minimum distance, generating polynomials and dimension of the minimum cyclic code generated by these primitive idempotents are discussed.
Abstract: Explicit expressions for all 2(nd+1) primitive idempotents in the ring 1 / ])[ (2 2 n n p p x x l GF R , where p and l are distinct odd primes such that d p l o n p n /) 2 () (2 , d ≥ 1 an integer, are obtained. The minimum distance, generating polynomials and dimension of the minimal cyclic codes generated by these primitive idempotents are also discussed. As example, we discuss the parameters of the minimal cyclic codes of length 22.
12 citations
TL;DR: In this paper, the authors show applications to solving equations in quotient rings, Hensel lifting, Hermite normal form computations, reduction of univariate polynomial lattices, and finding small generators in quadratic number rings.
Abstract: Strong Gröbner bases over Euclidean domains and even more general rings were first defined in the 1980s. Since that time, efficient ways to compute them, and a variety of applications, have appeared. In this note we show, via simple examples, applications to solving equations in quotient rings, Hensel lifting, Hermite normal form computations, reduction of univariate polynomial lattices, and finding small generators in quadratic number rings. Mathematics Subject Classification: 11C08, 11C20, 11D04, 11R11, 13B25, 13F07, 13P05, 13P10, 14Q99, 15A23, 15B36
12 citations
TL;DR: In this paper, it was shown that if A is a Gorenstein algebra such that Db has a recollement relative to Db(B) and C is a finite dimensional algebras, then B and C are GAs.
Abstract: Let A,B and C be finite dimensional algebras. In this paper, we prove that if A is a Gorenstein algebra such that Db(A) has a recollement relative to Db(B) and Db(C), then B and C are Gorenstein algebras. Mathematics Subject Classification: 18E30, 16G10; 16S10, 18G15
11 citations
10 citations
TL;DR: The results show that the skew cyclic codes are equivalent to either cyclic and quasi-cyclic codes over Galois rings, and a sufficient condition for 1-generator skew quasi-cycle codes to be free is determined.
Abstract: We mainly investigate the structures of skew cyclic and skew quasicyclic codes of arbitrary length over Galois rings. Similar to [5], our results show that the skew cyclic codes are equivalent to either cyclic and quasi-cyclic codes over Galois rings. Moreover, we give a necessary and sufficient condition for skew cyclic codes over Galois rings to be free. A sufficient condition for 1-generator skew quasi-cyclic codes to be free is also determined.
9 citations
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TL;DR: In this paper, a new algebraic structure, called KUSalgebra, is introduced and studied, and some properties of its properties are investigated, such as its properties and properties.
Abstract: The aim of this paper is to introduce and study new algebraic structure, called KUSalgebra and investigate some of its properties.
7 citations
TL;DR: In this article, it was shown that the classed pseudospectrum of matrix polynomials is equal to the unclassed pseudo-pseudo-pectrum.
Abstract: Pseudospectra associated with the generalized eigenvalue problems have been widely investigated in recent years. This paper is organized as follows. First, we prove for a class∈{Symmetric, Persymmetric, Toeplitz, SymToeplitz, Hankel, PersymHankel, Circulant}, we have the classed pseudospectrum of matrix is equal to the unclassed pseudospectrum because of the departure from singularity. Second, we prove the same results for classed pseudospectra of matrix polynomials. Mathematics Subject Classification: 65F15, 15A22, 65F15
TL;DR: It is claimed that the new powerful data structures MT and MA can play very important roles as powerful tools in the processing of big data (if arranged as a SM/SL, big temporal databases, etc), and will be useful in all branches of Sciences.
Abstract: Matrix theory has an unlimited volume of applications in all branches of Science, Engineering, Statistics, Optimization, Numerical Analysis, Computer Science, Medical Science, Economics, etc. The present day world dealing with big data (expanding very fast in 4Vs : Volume, Varity, Velocity and Veracity) needs advanced kind of logical and physical storage structures, advanced kind of heterogeneous data structures, new mathematical theories and new models, all these four together we call by 4Ns. In this paper the author introduces the notion of ‘solid matrix’ i.e. n-dimensional hyper-matrix, as a generalization of the classical matrix, and also the notion of ‘solid latrix’. Consequently the author develops the ‘Theory of Solid Matrices’ explaining various operation, properties and propositions on them. Then the author introduces two powerful data structures : a heterogeneous data structure MA and a homogeneous data structure MT. As a very important application of MA and MT, the author proposes a method on how to implement Solid Matrices, n-dimensional arrays, n-dimensional larrays etc. in a computer memory. It is claimed that the new powerful data structures MT and MA can play very important roles as powerful tools in the processing of big data (if arranged as a SM/SL), big temporal databases, etc. to the present data-dependent giant galaxies of organizations, institutions and individuals. It is also claimed that the ‘Theory of Matrices/Latrices’ will be useful in all branches of Sciences, in all branches of Engineering & Technology, Statistics, OR, Cosmology, Medical Sciences, etc. to list a few only out of many, for making better study and analysis if based upon complex computing.
TL;DR: In this article, the authors investigate all subdirect products of some groups that are not C8-groups and classify them as follows: Mathematics Subject Classification Classification: 20F99.
Abstract: In this paper we investigate all subdirect products of some groups that are not C8-groups. Mathematics Subject Classification: 20F99
TL;DR: In this article, the dimension of the subalgebra generated by the homomorphism of a semigroup S of degree n over a field F to the multiplicative semigroup of all n × n matrices with entries in F is studied.
Abstract: By a representation of a semigroup S of degree n over a field F we mean a homomorphism γ of S into the multiplicative semigroup of the algebra Mn(F) of all n × n matrices with entries in F. A representation is called faithful if it is injective. In this paper we focus our attention to the dimension of the subalgebra of Mn(F) generated by γ(S), where S is an n-element semigroup and γ is a faithful representation of S of degree n over a field F. In Section 2 we deal with the case when S and γ are arbitrary; in Section 3 we focus our attention to the case when S is left reductive and γ is the right regular representation of S.
TL;DR: In this article, the authors prove that M is commutative, i.e., M is a prime Γ-ring satisfying a certain assumption and D a nonzero derivation on M.
Abstract: Let M be a prime Γ-ring satisfying a certain assumption and D a nonzero derivation on M . Let f : M → M be a generalized derivation such that f is centralizing and commuting on a left ideal J of M . Then we prove that M is commutative. Mathematics Subject Classification: Primary 16N60; Secondary 16W25, 16U80
TL;DR: The authors refines the work on Gersgorin Discs in the article "Geo- metric multiplicities and GERSGORIN Discs", The American Mathematical Monthly, 120(2013), 452-455 by R. Marsli and F. Hall.
Abstract: This paper refines the work on Gersgorin Discs in the article "Geo- metric Multiplicities and Gersgorin Discs", The American Mathematical Monthly, 120(2013), 452-455 by R. Marsli and F. Hall. Some conse- quences of this refinement and examples are provided.
TL;DR: In this article classification subdirect products of some groups that are C8-groups are classified as follows: Mathematics Subject Classification (20F99): C8 -group (C8-group).
Abstract: In this paper we classification subdirect products of some groups that are C8-groups. Mathematics Subject Classification: 20F99
TL;DR: In this paper, the authors define a proper element p of a multiplicative lattice to be weakly primary if 0 ≤ ab ≤ p implies a ≤ p or b ≤ √ p.
Abstract: Let L be a multiplicative lattice. We define a proper element p of L to be weakly primary if 0 � ab ≤ p implies a ≤ p or b ≤ √ p. Our objective is to investigate the properties of weakly primary elements in multiplicative lattices.
TL;DR: In this article, the authors introduce the concept of comodule hom-coalgebras and show that these can be deformed from comodules via endomorphisms.
Abstract: We introduce the concept of comodule Hom-coalgebrasand show that comodule Hom-coalgebras can be deformed from comodule coalgebras via endomorphisms.
TL;DR: In this article, the authors give conditions which are both necessary and sufficient for a subsemigroup T to be left amenable to a cancellative, left-amenable semigroup S.
Abstract: Let T be a subsemigroup of a cancellative, left amenable semigroup S. We give conditions which are both necessary and sufficient for the subsemigroup T to be left amenable.
TL;DR: In this paper, it was shown that every absolute-valued algebra with left-unit verifying x(x) = (x)x is finite-dimensional of degree ≤ 4.
Abstract: We show that every absolute-valued algebra with left-unit verifying x(x) = (x)x is finite-dimensional of degree ≤ 4. In addition to the already known algebras R, C, ∗C, H, ∗H, ∗H(i, 1), O, ∗O, ∗O(i, 1) the list is completed by two new eight-dimensional algebras. Mathematics Subject Classification: 17A35, 17A36, 17A80
TL;DR: In this paper, a faithful multiplication and comultiplication module over a commutative ring R is defined and investigated, and some results on such modules are investigated. But the results are limited.
Abstract: Let M be a faithful multiplication and comultiplication module over a commutative ring R. In this paper we investigate some results on such modules. Mathematics Subject Classification: 13C05, 13C13, 13A15 , 13C99
TL;DR: In this article, the concept of prime and semiprime bi-ideals of ordered semigroups was introduced and characterizations of prime bi-ideal and regular of ordered semiigroups were given.
Abstract: In this paper we shall introduce the concept of prime and semiprime bi-ideals of ordered semigroups and we give characterizations of prime bi-ideal and regular of ordered semigroups
TL;DR: In this article, the E-order-preserving transformation semigroup on X (EOP(X)) is characterized as regular, left regular and right regular, and the purpose of this paper is to characterize when elements of EOP(x) are regular.
Abstract: Let (X, ≤) be a totally ordered set, E an arbitrary equivalence on X and T(X) the full transformation semigroup on X. We consider a subsemigroup of T(X) defined by EOP(X )= {α ∈ T(X ):( a, b) ∈ E and a ≤ b ⇒ (aα, bα) ∈ E and aα ≤ bα} which is called the E-order-preserving transformation semigroup on X. The purpose of this paper is to characterize when elements of EOP(X) are regular, left regular and right regular.
TL;DR: This article develops a mechanism for the derivation of individual player’s payoff functions in cooperative stochastic dynamic games with nontransferable payoffs, the first time that individual player's payoff functions are characterized in an analytically derivable form in such a framework.
Abstract: In cooperative dynamic games with non-transferable payoffs, the players’ agreed-upon cooperative actions would determine the resulting payoff that each player receives. This article develops a mechanism for the derivation of individual player’s payoff functions in cooperative stochastic dynamic games with nontransferable payoffs. This is the first time that individual player’s payoff functions are characterized in an analytically derivable form in such a framework. An illustrative example is provided. Mathematics Subject Classifications: 91A12, 91A25
TL;DR: Some results on semiprime fuzzy quasi-ideals with thresholds in ordered semigroups are established and some of characterization theorems are provided.
Abstract: In this paper, we introduce the concept of fuzzy quasi-ideals with thresholds \((\alpha ,\beta ]\) in ordered semigroups. By using this concept, some results of an ordered semigroup are discussed and some of characterization theorems are provided. Furthermore, we define the fuzzy subset \(f_{\alpha }^{\beta }\). We establish some results on semiprime fuzzy quasi-ideals with thresholds \((\alpha ,\beta ]\) in ordered semigroups and characterize completely regular ordered semigroups in terms of semiprime fuzzy quasi-ideals with thresholds \((\alpha ,\beta ]\) of \(S\).
TL;DR: In this article, it was shown that if a group of elements is a group such that the number of elements of order in the group is unique determined by the group's members, then the set of element orders of a group is determined by its members.
Abstract: Let \(G\) be a group and \(\omega(G)\) be the set of element orders of \(G\), \(k \in \omega(G)\) and \(s_k\) be the number of elements of order \(k\) in \(G\), \( nse(G) = \{s_k |k \in \omega(G)\}\), \(PSL(3, 2)\) and \(PSL(3, 4)\) are unique determined by \(nse(G)\). In this paper, we prove that if \(G\) is a group such that \(nse(G)=nse(PSU(3, 4))\), then \(G=PSU(3, 4)\).
TL;DR: In this paper it was shown that every absolute-valued algebra having both left unit and a non-zero central element is finite-dimensional, and that every algebra with both left-unit and nonzero central elements can be expressed in finite-dimension.
Abstract: We note that every absolute-valued algebra having both left-unit and a non-zero central element is finite-dimensional, next we specify. Mathematics Subject Classification: 17A35, 17A36
TL;DR: In this article, the maximum value of b(Γ(Zn)) is 0.99999999796427626489236243072661, where n is any positive integer upto fiftieth million.
Abstract: In this paper, we evaluate b(Γ(Zn)). Our main result is, we give maximum value of b(Γ(Zn)) is 0.99999999796427626489236243072661, where n is any positive integer upto fiftieth million. Mathematics Subject Classification: 05C25, 05C35, 05C70