Volume 14, Issue 1 (4-2019)
IJMSI 2019, 14(1): 147-157 |
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Babaei S, Payrovi S, Sengelen Sevim E. A Submodule-Based Zero Divisors Graph for Modules. IJMSI 2019; 14 (1) :147-157
URL: http://ijmsi.ir/article-1-956-en.html
URL: http://ijmsi.ir/article-1-956-en.html
Abstract:
Let $R$ be commutative ring with identity and $M$ be an $R$-module. The zero divisor graph of $M$ is denoted $Gamma{(M)}$. In this study, we are going to generalize the zero divisor graph $Gamma(M)$ to submodule-based zero divisor graph $Gamma(M, N)$ by replacing elements whose product is zero with elements whose product is in some submodules $N$ of $M$. The main objective of this paper is to study the interplay of the properties of submodule $N$ and the properties of $Gamma(M, N)$.
Type of Study: Research paper |
Subject:
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