Generalized \(\oplus\)-supplemented modules
Let \(R\) be a ring and \(M\) be a left \(R\)-module. \(M\) is called generalized \(\oplus\)- supplemented if every submodule of \(M\) has a generalized supplement that is a direct summand of \(M\). In this paper we give various properties of such modules. We show that any finite direct sum of gene...
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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/647 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-6472018-04-04T09:17:05Z Generalized \(\oplus\)-supplemented modules Calısıcı, Hamza Turkmen, Ergul generalized cover, generalized supplemented module, \(\oplus\)-supplemented module, generalized \(\oplus\)-supplemented module 16D10,16D99 Let \(R\) be a ring and \(M\) be a left \(R\)-module. \(M\) is called generalized \(\oplus\)- supplemented if every submodule of \(M\) has a generalized supplement that is a direct summand of \(M\). In this paper we give various properties of such modules. We show that any finite direct sum of generalized \(\oplus\)-supplemented modules is generalized \(\oplus\)-supplemented. If \(M\) is a generalized \(\oplus\)-supplemented module with \((D3)\), then every direct summand of \(M\) is generalized \(\oplus\)-supplemented. We also give some properties of generalized cover. 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/647 Algebra and Discrete Mathematics; Vol 10, No 2 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/647/181 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
generalized cover generalized supplemented module \(\oplus\)-supplemented module generalized \(\oplus\)-supplemented module 16D10,16D99 |
| spellingShingle |
generalized cover generalized supplemented module \(\oplus\)-supplemented module generalized \(\oplus\)-supplemented module 16D10,16D99 Calısıcı, Hamza Turkmen, Ergul Generalized \(\oplus\)-supplemented modules |
| topic_facet |
generalized cover generalized supplemented module \(\oplus\)-supplemented module generalized \(\oplus\)-supplemented module 16D10,16D99 |
| format |
Article |
| author |
Calısıcı, Hamza Turkmen, Ergul |
| author_facet |
Calısıcı, Hamza Turkmen, Ergul |
| author_sort |
Calısıcı, Hamza |
| title |
Generalized \(\oplus\)-supplemented modules |
| title_short |
Generalized \(\oplus\)-supplemented modules |
| title_full |
Generalized \(\oplus\)-supplemented modules |
| title_fullStr |
Generalized \(\oplus\)-supplemented modules |
| title_full_unstemmed |
Generalized \(\oplus\)-supplemented modules |
| title_sort |
generalized \(\oplus\)-supplemented modules |
| description |
Let \(R\) be a ring and \(M\) be a left \(R\)-module. \(M\) is called generalized \(\oplus\)- supplemented if every submodule of \(M\) has a generalized supplement that is a direct summand of \(M\). In this paper we give various properties of such modules. We show that any finite direct sum of generalized \(\oplus\)-supplemented modules is generalized \(\oplus\)-supplemented. If \(M\) is a generalized \(\oplus\)-supplemented module with \((D3)\), then every direct summand of \(M\) is generalized \(\oplus\)-supplemented. We also give some properties of generalized cover. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/647 |
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AT calısıcıhamza generalizedoplussupplementedmodules AT turkmenergul generalizedoplussupplementedmodules |
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2024-04-12T06:26:34Z |
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2024-04-12T06:26:34Z |
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1796109220994613248 |