A generalization of pure submodules

چکیده مقاله

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 S-pure if there exists an s ∈ S such that s(N ∩ IM) ⊆ IN for every ideal I of R. Also, We say that M is fully S-pure if every submodule of M is S-pure. © 2020, University of Guilan. All rights reserved.