University of Guilan Journal of Algebra and Related Topics 2345-3931 8 2 2020 12 01 A generalization of pure submodules 1 8 4273 10.22124/jart.2020.17279.1215 EN F. Farshadifar University of Farhangian, Tehran, Iran. Journal Article 2020 07 31 ‎Let $R$ be a commutative ring with identity‎, ‎$S$ a multiplicatively closed subset of $R$‎, ‎and $M$ be an $R$-module‎.<br /> ‎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.<br /> ‎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. https://jart.guilan.ac.ir/article_4273_4b19a029613bb0a34b66dbc38bb6321c.pdf