University of GuilanJournal of Algebra and Related Topics2345-39318220201201A generalization of pure submodules18427310.22124/jart.2020.17279.1215ENF.FarshadifarUniversity of Farhangian, Tehran, Iran.Journal Article20200731Let $R$ 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