A generalization of pure submodules

‎Let R be a commutative ring with identity‎, ‎S a multiplicatively closed subset of R‎, ‎and M be an R-module‎. ‎The goal of this work is to introduce the notion of S-pure submodules of M as a generalization of pure submodules of M and prove a number of results concerning of this class of modules‎. ‎We say that a submodule N of M is \emph {S-pure} if there exists an s \in S such that s(N \cap IM) \subseteq IN for every ideal I of R‎. ‎Also‎, ‎We say that M is \emph{fully S-pure} if every submodule of M is S-pure‎.

Keywords:

Pure submodule‎ , ‎S-pure submodule‎ , ‎fully S-pure module