فهرست نشریات علمی دسترسی آزاد ایران

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.