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 ∈ 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 a graded jgr-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.