A Submodule-Based Zero Divisors Graph for Modules

Author(s):

S. Babaei , Sh. Payrovi* , E. Sengelen Sevim

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
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 $Gamma(M‎, ‎N)$‎.
Keywords:

Zero-divisor graph‎ , ‎Submodule-based zero-divisor graph‎ , ‎ Semi simple module.

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:14 Issue: 1, May 2019
Pages:
147 to 157
https://www.magiran.com/p1956542