On S-submodules of modules over commutative rings

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R and M be an R-module. In this paper, we introduce and study the notion of S-submodules as a generalization of S-ideals. We define a proper submodule N of M to be an S-submodule if whenever sm ? N for some s ? S and m ? M, we have m ? N. Several properties, characterizations and examples of S-submodules are given.