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.
Farshadifar, F. (2020). A generalization of pure submodules. Journal of Algebra and Related Topics, 8(2), 1-8. doi: 10.22124/jart.2020.17279.1215
MLA
F. Farshadifar. "A generalization of pure submodules". Journal of Algebra and Related Topics, 8, 2, 2020, 1-8. doi: 10.22124/jart.2020.17279.1215
HARVARD
Farshadifar, F. (2020). 'A generalization of pure submodules', Journal of Algebra and Related Topics, 8(2), pp. 1-8. doi: 10.22124/jart.2020.17279.1215
VANCOUVER
Farshadifar, F. A generalization of pure submodules. Journal of Algebra and Related Topics, 2020; 8(2): 1-8. doi: 10.22124/jart.2020.17279.1215
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