A generalization of supplemented modules
Let \(R\) be an arbitrary ring with identity and \(M\) a right \(R\)-module. In this paper, we introduce a class of modules which is an analogous of \(\delta\)-supplemented modules defined by Kosan. The module \(M\) is called principally \(\delta\)-supplemented, for all \(m\in M\) there exists a s...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/660 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-6602018-04-04T09:21:34Z A generalization of supplemented modules Inankil, Hatice Halıcıoglu, Sait Harmanci, Abdullah supplemented modules, \(\delta\)-supplemented modules, principally \(\delta\)-supplemented modules, semiperfect modules, \(\delta\)-semiperfect modules, principally \(\delta\)-semiperfect modules 16U80 Let \(R\) be an arbitrary ring with identity and \(M\) a right \(R\)-module. In this paper, we introduce a class of modules which is an analogous of \(\delta\)-supplemented modules defined by Kosan. The module \(M\) is called principally \(\delta\)-supplemented, for all \(m\in M\) there exists a submodule \(A\) of \(M\) with \(M = mR + A\) and \((mR)\cap A\) \(\delta\)-small in \(A\). We prove that some results of \(\delta\)-supplemented modules can be extended to principally \(\delta\)-supplemented modules for this general settings. We supply some examples showing that there are principally \(\delta\)-supplemented modules but not \(\delta\)-supplemented. We also introduce principally \(\delta\)-semiperfect modules as a generalization of \(\delta\)-semiperfect modules and investigate their properties. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/660 Algebra and Discrete Mathematics; Vol 11, No 1 (2011) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/660/194 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2018-04-04T09:21:34Z |
| collection |
OJS |
| language |
English |
| topic |
supplemented modules \(\delta\)-supplemented modules principally \(\delta\)-supplemented modules semiperfect modules \(\delta\)-semiperfect modules principally \(\delta\)-semiperfect modules 16U80 |
| spellingShingle |
supplemented modules \(\delta\)-supplemented modules principally \(\delta\)-supplemented modules semiperfect modules \(\delta\)-semiperfect modules principally \(\delta\)-semiperfect modules 16U80 Inankil, Hatice Halıcıoglu, Sait Harmanci, Abdullah A generalization of supplemented modules |
| topic_facet |
supplemented modules \(\delta\)-supplemented modules principally \(\delta\)-supplemented modules semiperfect modules \(\delta\)-semiperfect modules principally \(\delta\)-semiperfect modules 16U80 |
| format |
Article |
| author |
Inankil, Hatice Halıcıoglu, Sait Harmanci, Abdullah |
| author_facet |
Inankil, Hatice Halıcıoglu, Sait Harmanci, Abdullah |
| author_sort |
Inankil, Hatice |
| title |
A generalization of supplemented modules |
| title_short |
A generalization of supplemented modules |
| title_full |
A generalization of supplemented modules |
| title_fullStr |
A generalization of supplemented modules |
| title_full_unstemmed |
A generalization of supplemented modules |
| title_sort |
generalization of supplemented modules |
| description |
Let \(R\) be an arbitrary ring with identity and \(M\) a right \(R\)-module. In this paper, we introduce a class of modules which is an analogous of \(\delta\)-supplemented modules defined by Kosan. The module \(M\) is called principally \(\delta\)-supplemented, for all \(m\in M\) there exists a submodule \(A\) of \(M\) with \(M = mR + A\) and \((mR)\cap A\) \(\delta\)-small in \(A\). We prove that some results of \(\delta\)-supplemented modules can be extended to principally \(\delta\)-supplemented modules for this general settings. We supply some examples showing that there are principally \(\delta\)-supplemented modules but not \(\delta\)-supplemented. We also introduce principally \(\delta\)-semiperfect modules as a generalization of \(\delta\)-semiperfect modules and investigate their properties. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/660 |
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2025-12-02T15:46:26Z |
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