Modules whose maximal submodules have \(\tau\)-supplements
Let \(R\) be a ring and \(\tau\) be a preradical for the category of left \(R\)-modules. In this paper, we study on modules whose maximal submodules have \(\tau\)-supplements. We give some characterizations of these modules in terms their certain submodules, so called \(\tau\)-local submodules. For...
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| Datum: | 2018 |
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| 1. Verfasser: | |
| 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/646 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | Let \(R\) be a ring and \(\tau\) be a preradical for the category of left \(R\)-modules. In this paper, we study on modules whose maximal submodules have \(\tau\)-supplements. We give some characterizations of these modules in terms their certain submodules, so called \(\tau\)-local submodules. For some certain preradicals \(\tau\), i.e. \(\tau=\delta\) and idempotent \(\tau\), we prove that every maximal submodule of \(M\) has a \(\tau\)-supplement if and only if every cofinite submodule of \(M\) has a \(\tau\)-supplement. For a radical \(\tau\) on \(\operatorname{R-Mod}\), we prove that, for every \(R\)-module every submodule is a \(\tau\)-supplement if and only if \(R/\tau(R)\) is semisimple and \(\tau\) is hereditary. |
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