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 grad M ( N ) and grad M ( K ) are graded coprime.