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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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/647 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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. |
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