GRADED SEMIPRIME SUBMODULES OVER NON-COMMUTATIVE GRADED RINGS

Let G be a group with identity e, R be an associative graded ring and M be a G-graded R-module. In this article, we intruduce the concept of graded semiprimesubmodules over non-commutative graded rings. First, we study graded prime R-modulesover non-commutative graded rings and we get some properties of such graded modules.Second, we study graded semiprime and graded radical submodules of graded R-modules.For example, we give some equivalent conditions for a graded module to have zero gradedradical submodule.

کلیدواژه ها:

graded prime module ، graded radical submodule ، graded semiprime submodule