gw-S-prime submodules

Let R be a ring with identity and S ⊆ R be a multiplicative closed subset. Let M be an R-module. Sevim et al. [15] introduced the concept of S-prime submodule. A submodule P of M with (P :R M) ∩ S = ϕ is called an S-prime submodule if there is an s ∈ S such that am ∈ P implies sa ∈ (P :R M) or sm ∈ P. In this paper, we introduce the notion of gw-S-prime submodule. This class ofsubmodules is a generalization of S-prime submodules. We present some basic properties of gw-S-prime submodules. We also investigate the relationship of gw-Sprime submodule with valuation modules. We further study some propeties of gw-Sprimesubmodules under R-module homomorphism and direct product of modules.