AU - Babaei, S. AU - Payrovi, Sh. AU - Sengelen Sevim, E. TI - A Submodule-Based Zero Divisors Graph for Modules PT - JOURNAL ARTICLE TA - IJMSI JN - IJMSI VO - 14 VI - 1 IP - 1 4099 - http://ijmsi.ir/article-1-956-en.html 4100 - http://ijmsi.ir/article-1-956-en.pdf SO - IJMSI 1 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 $Gamma(M‎, ‎N)$‎. CP - IRAN IN - Department of Mathematics,‎ Imam Khomeini International University, ‎Postal Code‎: ‎34149-1-6818‎, ‎Qazvin‎, ‎Iran LG - eng PB - IJMSI PG - 147 PT - Research paper YR - 2019