Graded semiprime multiplication modules

Abstract

Let $M$ be a $G$-graded $R$-module. In this article, we introduce the concept of graded semiprime multiplication modules. A graded $R$-module $M$ is said to be graded semiprime multiplication if $M$ has no graded semiprime $R$-submodules or for every graded semiprime $R$-submodule $N$ of $M$, $N=IM$ for some graded ideal $I$ of $R$. We introduce several results concerning graded semiprime submodules and we investigate them to present several results on graded semiprime multiplication modules.