On graded J_{gr}-classical prime submodules

Let G be a group with identity e. Let R be a G-graded commutative ring with identity 1 and M a graded R-module. A proper graded submodule C of M is called a graded classical prime submodule if whenever r,s\in h(R) and m\in h(M) with rsm\in C, then either rm\in C or sm\in C. In this paper, we introduce the concept of graded J_{gr}-classical prime submodule as a new generalization of graded classical submodule and we give some results concerning such graded modules. We say that a proper graded submodule N of M is \textit{a graded }J_{gr}\textit{-classical prime submodule of \ }M if whenever rsm\in N where r,s\in h(R) and m\in h(M), then either rm\in N+J_{gr}(M) or sm\in N+J_{gr}(M), where J_{gr}(M) is the graded Jacobson radical.

On graded J_{gr}-classical prime submodules Keywords:

Graded J_{gr}-classical prime submodule , Graded classical prime submodule , Graded prime