RT - Journal Article T1 - A Submodule-Based Zero Divisors Graph for Modules JF - IJMSI YR - 2019 JO - IJMSI VO - 14 IS - 1 UR - http://ijmsi.ir/article-1-956-en.html SP - 147 EP - 157 K1 - Zero-divisor graph‎ K1 - ‎Submodule-based zero-divisor graph‎ K1 - ‎ Semi simple module. AB - ‎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 $Gamma(M‎, ‎N)$‎. LA eng UL http://ijmsi.ir/article-1-956-en.html M3 ER -