@article {
author = {Farshadifar, F.},
title = {A generalization of pure submodules},
journal = {Journal of Algebra and Related Topics},
volume = {8},
number = {2},
pages = {1-8},
year = {2020},
publisher = {University of Guilan},
issn = {2345-3931},
eissn = {2382-9877},
doi = {10.22124/jart.2020.17279.1215},
abstract = {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},
url = {https://jart.guilan.ac.ir/article_4273.html},
eprint = {https://jart.guilan.ac.ir/article_4273_4b19a029613bb0a34b66dbc38bb6321c.pdf}
}