ON GRADED Jgr-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 2 h(R) and m 2 h(M) with rsm 2 C, then either rm 2 C or sm 2 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 a graded Jgr-classical prime submodule of M if whenever rsm 2 N where r; s 2 h(R) and m 2 h(M), then either rm 2 N + Jgr(M) or sm 2 N + Jgr(M), where Jgr(M) is the graded Jacobson radical.