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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2018, Volume 26, Issue 1, Pages 110–123 (Mi adm674)

RESEARCH ARTICLE

On the saturations of submodules

Lokendra Paudela, Simplice Tchamnab

a Department of Mathematics, The University of Akron, Akron, OH 44325, USA
b Department of Mathematics, Georgia College & State University, Campus Box 017, Milledgeville, GA 31061, USA

Abstract: 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 $A_{[\tau] }= \{x\in S\colon A for some t\in \tau\}$, 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: saturation, star operation, ring extension, prime spectrum, localization, flat module.

 Funding Agency Grant Number Georgia College FY 16 The second author was supported by the Georgia College faculty development travel grant FY 16.

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MSC: 13A15, 13A18, 13B02
Revised: 17.01.2017
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Citation: Lokendra Paudel, Simplice Tchamna, “On the saturations of submodules”, Algebra Discrete Math., 26:1 (2018), 110–123

Citation in format AMSBIB
\Bibitem{PauTch18}
\by Lokendra~Paudel, Simplice~Tchamna
\paper On the saturations of submodules
\jour Algebra Discrete Math.
\yr 2018
\vol 26
\issue 1
\pages 110--123