Amply (weakly) Goldie-Rad-supplemented modules
Let \(R\) be a ring and \(M\) be a right \(R\)-module. We say a submodule \(S\) of \(M\) is a \textit{(weak) Goldie-Rad-supplement} of a submodule \(N\) in \(M\), if \(M=N+S\), \((N\cap S \leq Rad(M))\) \(N\cap S\leq Rad(S)\) and \(N\beta^{**} S\), and \(M\) is called amply (weakly) Goldie-Rad-supp...
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| Дата: | 2016 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2016
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/59 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-592016-11-15T13:03:03Z Amply (weakly) Goldie-Rad-supplemented modules Takıl Mutlu, Figen Supplement submodule, Goldie-Rad-Supplement submodule, amply Goldie-Rad-Supplemented module 16D10, 16D40, 16D70 Let \(R\) be a ring and \(M\) be a right \(R\)-module. We say a submodule \(S\) of \(M\) is a \textit{(weak) Goldie-Rad-supplement} of a submodule \(N\) in \(M\), if \(M=N+S\), \((N\cap S \leq Rad(M))\) \(N\cap S\leq Rad(S)\) and \(N\beta^{**} S\), and \(M\) is called amply (weakly) Goldie-Rad-supplemented if every submodule of \(M\) has ample (weak) Goldie-Rad-supplements in \(M\). In this paper we study various properties of such modules. We show that every distributive projective weakly Goldie-Rad-Supplemented module is amply weakly Goldie-Rad-Supplemented. We also show that if \(M\) is amply (weakly) Goldie-Rad-supplemented and satisfies DCC on (weak) Goldie-Rad-supplement submodules and on small submodules, then \(M\) is Artinian. Lugansk National Taras Shevchenko University This study was supported by Anadolu University Scientific Research Projects Commission under the grant no:1505F225. 2016-11-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/59 Algebra and Discrete Mathematics; Vol 22, No 1 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/59/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/59/129 Copyright (c) 2016 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
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| datestamp_date |
2016-11-15T13:03:03Z |
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OJS |
| language |
English |
| topic |
Supplement submodule Goldie-Rad-Supplement submodule amply Goldie-Rad-Supplemented module 16D10 16D40 16D70 |
| spellingShingle |
Supplement submodule Goldie-Rad-Supplement submodule amply Goldie-Rad-Supplemented module 16D10 16D40 16D70 Takıl Mutlu, Figen Amply (weakly) Goldie-Rad-supplemented modules |
| topic_facet |
Supplement submodule Goldie-Rad-Supplement submodule amply Goldie-Rad-Supplemented module 16D10 16D40 16D70 |
| format |
Article |
| author |
Takıl Mutlu, Figen |
| author_facet |
Takıl Mutlu, Figen |
| author_sort |
Takıl Mutlu, Figen |
| title |
Amply (weakly) Goldie-Rad-supplemented modules |
| title_short |
Amply (weakly) Goldie-Rad-supplemented modules |
| title_full |
Amply (weakly) Goldie-Rad-supplemented modules |
| title_fullStr |
Amply (weakly) Goldie-Rad-supplemented modules |
| title_full_unstemmed |
Amply (weakly) Goldie-Rad-supplemented modules |
| title_sort |
amply (weakly) goldie-rad-supplemented modules |
| description |
Let \(R\) be a ring and \(M\) be a right \(R\)-module. We say a submodule \(S\) of \(M\) is a \textit{(weak) Goldie-Rad-supplement} of a submodule \(N\) in \(M\), if \(M=N+S\), \((N\cap S \leq Rad(M))\) \(N\cap S\leq Rad(S)\) and \(N\beta^{**} S\), and \(M\) is called amply (weakly) Goldie-Rad-supplemented if every submodule of \(M\) has ample (weak) Goldie-Rad-supplements in \(M\). In this paper we study various properties of such modules. We show that every distributive projective weakly Goldie-Rad-Supplemented module is amply weakly Goldie-Rad-Supplemented. We also show that if \(M\) is amply (weakly) Goldie-Rad-supplemented and satisfies DCC on (weak) Goldie-Rad-supplement submodules and on small submodules, then \(M\) is Artinian. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2016 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/59 |
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