A Generalization of Graded Prime Submodules over Non-Commutative Graded Rings

Abstract

Let $G$ be a group with identity $e$. Let $R$ be an associative $G$-graded ring and $M$ be a $G$-graded $R$-module. In this article, we intruduce the concept of graded 2-absorbing submodules as a generalization of graded prime submodules over non-commutative graded rings. Moreover, we get some properties of such graded submodules.