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- W3102293494 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." @default.
- W3102293494 created "2020-11-23" @default.
- W3102293494 creator A5065171438 @default.
- W3102293494 date "2020-12-01" @default.
- W3102293494 modified "2023-09-23" @default.
- W3102293494 title "A generalization of pure submodules" @default.
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- W3102293494 doi "https://doi.org/10.22124/jart.2020.17279.1215" @default.
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