On a generalization of graded 2-absorbing submodules

Abstract

"Let G be a group with identity e. Let R be a G-graded commutative ring with nonzero identity and M a graded R-module. In this paper, we introduce the concept of graded G2-absorbing submodule as a new generalization of a graded 2-absorbing submodule on the one hand and a generalization of a graded primary submodule on other hand. We give a number of results concerning these classes of graded submodules and their homogeneous components. In fact, our objective is to investigate graded G2-absorbing submodules and examine in particular when graded submodules are graded G2-absorbing submodules. For example, we give a characterization of graded G2-absorbing submodules. We also study the behaviour of graded G2-absorbing submodules under graded homomorphisms and under localization."