Geodesic
On the saturations of submodules
Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 110-123

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Let $R\subseteq S$ be a ring extension, and let $A$ be an $R$-submodule of $S$. The saturation of $A$ (in $S$) by $\tau$ is set $A_{[\tau] }= \left\{x\in S\colon A \text{ for some } t\in \tau\right\}$, where $\tau$ is a multiplicative subset of $R$. We study properties of saturations of $R$-submodules of $S$. We use this notion of saturation to characterize star operations $\star$ on ring extensions $R\subseteq S$ satisfying the relation $(A\cap B)^{\star} = A^{\star}\cap B^{\star}$ whenever $A$ and $B$ are two $R$-submodules of $S$ such that $AS= BS = S$.
Keywords: star operation, ring extension, prime spectrum, localization, flat module.
Mots-clés : saturation 
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     author = {Lokendra Paudel and Simplice Tchamna},
     title = {On the saturations of submodules},
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     volume = {26},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_26_1_a10/}
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Lokendra Paudel; Simplice Tchamna. On the saturations of submodules. Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 110-123. http://geodesic.mathdoc.fr/item/ADM_2018_26_1_a10/