Graded coprime submodules

Let G be a group. Let R be a G-graded commutative ring with identity, and let M be a G-graded module over R. Two graded submodules N and K of graded module M are called graded coprime whenever N + K = M. In this paper, some properties of graded coprime submodules are discussed. For example, we show that if M is a graded finitely generated module, then two graded submodules N and K of M are graded coprime if and only if gradM(N) and gradM(K) are graded coprime.