On graded $I_e$-prime submodules of graded modules over graded commutative rings

Abstract

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with identity and $M$ a graded $R$-module. In this paper, we introduce the concept of graded $I_e$-prime submodule as a generalization of a graded prime submodule for $I={\oplus }_{g\in G}{I}_g$ a fixed graded ideal of $R$. We give a number of results concerning of these classes of graded submodules and their homogeneous components. A proper graded submodule $N$ of $M$ is said to be a graded $I_e$-prime submodule of $M$ if whenever and $m_h\in h(M)$ with $r_g{m}_h\in N-I_{e}N,$ then either $r_g\in (N{:}_{R}M)$ or $m_h\in N.$

Cited by in corpus (1)

• Graded Lie-Rinehart algebras