On the saturations of submodules
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 \(A_{[\tau] }= \left\{x\in S : tx\in A \text{ for some } t\in \tau\right\}\), where \(\tau\) is a multiplicative subset of \(R\). We study properties of satu...
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| Date: | 2018 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/361 |
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| Journal Title: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-3612018-10-20T08:02:25Z On the saturations of submodules Paudel, Lokendra Tchamna, Simplice saturation, star operation, ring extension 13A15, 13A18, 13B02 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 \(A_{[\tau] }= \left\{x\in S : tx\in A \text{ for some } t\in \tau\right\}\), 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 \(AS= BS = S\). Lugansk National Taras Shevchenko University 2018-10-20 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/361 Algebra and Discrete Mathematics; Vol 26, No 1 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/361/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/361/151 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-10-20T08:02:25Z |
| collection |
OJS |
| language |
English |
| topic |
saturation star operation ring extension 13A15 13A18 13B02 |
| spellingShingle |
saturation star operation ring extension 13A15 13A18 13B02 Paudel, Lokendra Tchamna, Simplice On the saturations of submodules |
| topic_facet |
saturation star operation ring extension 13A15 13A18 13B02 |
| format |
Article |
| author |
Paudel, Lokendra Tchamna, Simplice |
| author_facet |
Paudel, Lokendra Tchamna, Simplice |
| author_sort |
Paudel, Lokendra |
| title |
On the saturations of submodules |
| title_short |
On the saturations of submodules |
| title_full |
On the saturations of submodules |
| title_fullStr |
On the saturations of submodules |
| title_full_unstemmed |
On the saturations of submodules |
| title_sort |
on the saturations of submodules |
| description |
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 \(A_{[\tau] }= \left\{x\in S : tx\in A \text{ for some } t\in \tau\right\}\), 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 \(AS= BS = S\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/361 |
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AT paudellokendra onthesaturationsofsubmodules AT tchamnasimplice onthesaturationsofsubmodules |
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2025-07-17T10:33:43Z |
| last_indexed |
2025-07-17T10:33:43Z |
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1837889931002773504 |