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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| Datum: | 2018 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/660 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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