On graded n− absorbing submodules

Abstract

Let G be a group with identity e. Let R be a G− graded commutative ring, M be a graded R− module and n be a positive integer. In this article, we introduce and study the concepts of graded n− absorbing submodules. Various properties of graded n− absorbing submodules are considered. For example, we show that if R is a Noetherian G− graded ring and M is a finitely generated graded R− module, then every nonzero proper graded submodule of M is a graded n− absorbing submodule of M for some positive integer n.