On a variation of \(\oplus\)-supplemented modules
Let \(R\) be a ring and \(M\) be an \(R\)-module. \(M\) is called \(\oplus_{ss}\)-supplemented if every submodule of \(M\) has a \(ss\)-supplement that is a direct summand of \(M\). In this paper, the basic properties and characterizations of \(\oplus_{ss}\)-supplemented modules are provided. In par...
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Lugansk National Taras Shevchenko University
2024
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oai:ojs.admjournal.luguniv.edu.ua:article-22732024-09-23T09:29:11Z On a variation of \(\oplus\)-supplemented modules Kaynar, Engin \(ss\)-supplement submodule, \(\oplus_{ss}\)-supplemented module 16D10, 16D60, 16D99 Let \(R\) be a ring and \(M\) be an \(R\)-module. \(M\) is called \(\oplus_{ss}\)-supplemented if every submodule of \(M\) has a \(ss\)-supplement that is a direct summand of \(M\). In this paper, the basic properties and characterizations of \(\oplus_{ss}\)-supplemented modules are provided. In particular, it is shown that \((1)\) if a module \(M\) is \(\oplus_{ss}\)-supplemented, then \(Rad(M)\) is semisimple and \(Soc(M)\unlhd M\); \((2)\) every direct sum of \(ss\)-lifting modules is \(\oplus_{ss}\)-supplemented; \((3)\) a commutative ring \(R\) is an artinian serial ring with semisimple radical if and only if every left \(R\)-module is \(\oplus_{ss}\)-supplemented. Lugansk National Taras Shevchenko University 2024-09-23 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2273 10.12958/adm2273 Algebra and Discrete Mathematics; Vol 38, No 1 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2273/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2273/1192 Copyright (c) 2024 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2024-09-23T09:29:11Z |
| collection |
OJS |
| language |
English |
| topic |
\(ss\)-supplement submodule \(\oplus_{ss}\)-supplemented module 16D10 16D60 16D99 |
| spellingShingle |
\(ss\)-supplement submodule \(\oplus_{ss}\)-supplemented module 16D10 16D60 16D99 Kaynar, Engin On a variation of \(\oplus\)-supplemented modules |
| topic_facet |
\(ss\)-supplement submodule \(\oplus_{ss}\)-supplemented module 16D10 16D60 16D99 |
| format |
Article |
| author |
Kaynar, Engin |
| author_facet |
Kaynar, Engin |
| author_sort |
Kaynar, Engin |
| title |
On a variation of \(\oplus\)-supplemented modules |
| title_short |
On a variation of \(\oplus\)-supplemented modules |
| title_full |
On a variation of \(\oplus\)-supplemented modules |
| title_fullStr |
On a variation of \(\oplus\)-supplemented modules |
| title_full_unstemmed |
On a variation of \(\oplus\)-supplemented modules |
| title_sort |
on a variation of \(\oplus\)-supplemented modules |
| description |
Let \(R\) be a ring and \(M\) be an \(R\)-module. \(M\) is called \(\oplus_{ss}\)-supplemented if every submodule of \(M\) has a \(ss\)-supplement that is a direct summand of \(M\). In this paper, the basic properties and characterizations of \(\oplus_{ss}\)-supplemented modules are provided. In particular, it is shown that \((1)\) if a module \(M\) is \(\oplus_{ss}\)-supplemented, then \(Rad(M)\) is semisimple and \(Soc(M)\unlhd M\); \((2)\) every direct sum of \(ss\)-lifting modules is \(\oplus_{ss}\)-supplemented; \((3)\) a commutative ring \(R\) is an artinian serial ring with semisimple radical if and only if every left \(R\)-module is \(\oplus_{ss}\)-supplemented. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2024 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2273 |
| work_keys_str_mv |
AT kaynarengin onavariationofoplussupplementedmodules |
| first_indexed |
2024-09-24T04:03:45Z |
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2024-09-24T04:03:45Z |
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1820651918636089344 |