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

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

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