Le Matematiche (Dec 2015)
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.
