**Volume 8 (2020-2021)**

**Volume 7 (2019-2020)**

**Volume 6 (2018-2019)**

**Volume 5 (2017-2018)**

**Volume 4 (2016-2017)**

**Volume 3 (2015-2016)**

**Volume 2 (2014-2015)**

**Volume 1 (2013-2014)**

# Author = Naghipour, A
Number of Articles: 4

##### 1. ON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS

*Volume 7, Issue 1 , Summer and Autumn 2019, , Pages 51-68*

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**Abstract **

Let $R$ be a ring (not necessarily commutative) with nonzero identity. We define $\Gamma(R)$ to be the graph with vertex set $R$ in which two distinct vertices $x$ and $y$ are adjacent if and only if there exist unit elements $u,v$ of $R$ such that $x+uyv$ is a unit of $R$. In this paper, basic properties ...
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##### 2. THE ZERO-DIVISOR GRAPH OF A MODULE

*Volume 4, Issue 2 , Winter and Spring 2017, , Pages 155-171*

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**Abstract **

Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, sayΓ(RM), such that when M=R, Γ(RM) coincide with the zero-divisor graph of R. Many well-known results by D.F. Anderson and P.S. Livingston have been generalized for ...
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##### 3. GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES

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

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**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 ...
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##### 4. SOME RESULTS ON STRONGLY PRIME SUBMODULES

*Volume 1, Issue 2 , Winter and Spring 2014, , Pages 79-89*