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 introduce the concept of graded semiprime submodules over non-commutative graded rings. First, we study graded prime Rmodules over 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 graded radical submodule.