A Submodule-Based Zero Divisor Graph for Modules

Abstract

Let R be a commutative ring with identity and M be an R-module. The zero divisor graph of M is denoted by 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 submodule 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).