On graded -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∈h(R) and m∈h(M) with rsm∈C, then either rm∈C or sm∈C. In this paper, we introduce the concept of graded Jgr-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 }Jgr\textit{-classical prime submodule of \ }M if whenever rsm∈N where r,s∈h(R) and m∈h(M), then either rm∈N+Jgr(M) or sm∈N+Jgr(M), where Jgr(M) is the graded Jacobson radical.