##### ON THE MAXIMAL SPECTRUM OF A MODULE

H. Ansari-Toroghy; S. keyvani

Volume 5, Issue 1 , September 2017, , Pages 73-84
##### Abstract
Let $R$ be a commutative ring with identity. The purpose of this paper is to introduce and study two classes of modules over $R$, called $\mbox{Max}$-injective and $\mbox{Max}$-strongly top modules and explore some of their basic properties. Our concern is to extend some properties of $X$-injective and ...  Read More

##### AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS

Volume 3, Issue 1 , September 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

##### GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES

A.R. Naghipour

Volume 3, Issue 1 , September 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

##### SOME RESULTS ON STRONGLY PRIME SUBMODULES

A.R. Naghipour

Volume 1, Issue 2 , January 2014, , Pages 79-89
##### Abstract
Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)y P$ for $x, y M$, implies that $x P$ or $y P$. In this paper, we study more properties of strongly prime submodules. It is shown that a ...  Read More