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 ofm as a generalization of pure submodules of m and prove a number of results concerning of this class of modules. we say that asubmodule n of m is s-pure if there exists an s ∈ s such thats(n ∩ im) ⊆ in for every ideal i of r. also, we say that m isfully s-pure if every submodule of m is s-pure.