1. THE CONCEPT OF (I; J)-COHEN MACAULAY MODULES

M. Aghapournahr; Kh. Ahmadi-amoli; M. Sadeghi

Volume 3, Issue 1 , Summer and Autumn 2015, Pages 1-10

Abstract
  ‎We introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎We also introduce the concept of $(I,J)$-Cohen--Macaulay modules as a generalization of concept of Cohen--Macaulay ...  Read More

2. AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS

S. Karimzadeh; R. Nekooei

Volume 3, Issue 1 , Summer and Autumn 2015, Pages 11-22

Abstract
  In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going ...  Read More

3. GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES

A.R. Naghipour

Volume 3, Issue 1 , Summer and Autumn 2015, Pages 23-30

Abstract
  The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem ...  Read More

4. GENERALIZED JOINT HIGHER-RANK NUMERICAL RANGE

H. R. Afshin; S. Bagheri; M. A. Mehrjoofard

Volume 3, Issue 1 , Summer and Autumn 2015, Pages 31-38

Abstract
  The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the ...  Read More

5. ANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS

M. Baziar

Volume 3, Issue 1 , Summer and Autumn 2015, Pages 39-47

Abstract
  In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. Weobserve that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ isconnected and diam$Bbb{AG}_*(_RM)leq 3$. Moreover, if $Bbb{AG}_*(_RM)$ contains a cycle, then $mbox{gr}Bbb{AG}_*(_RM)leq ...  Read More

6. HvMV-ALGEBRAS II

M. Bakhshi

Volume 3, Issue 1 , Summer and Autumn 2015, Pages 49-64

Abstract
  In this paper, we continue our study on HvMV-algebras. The quotient structure of an HvMV-algebra by a suitable types of congruences is studied and some properties and related results are given. Some homomorphism theorems are given, as well. Also, the fundamental HvMV-algebra and the direct product of ...  Read More

7. FUZZY NEXUS OVER AN ORDINAL

A. A. Estaji; T. Haghdadi; J. Farokhi Ostad

Volume 3, Issue 1 , Summer and Autumn 2015, Pages 65-82

Abstract
  ‎‎In this paper‎, ‎we define fuzzy subnexuses over a nexus $N$‎. ‎Define and study the notions of the prime fuzzy subnexuses and the fractions‎‎induced by them‎. ‎Finally‎, ‎we show that if S is a meet‎‎closed subset of the set Fsub(N), ‎of ...  Read More

8. COMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS

M. Jalali; A. R. Ashrafi

Volume 3, Issue 1 , Summer and Autumn 2015, Pages 88-95

Abstract
  Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, ...  Read More