Rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication
Let \(R\) be a ring with an endomorphism \(\sigma\). We introduce \((\overline{\sigma}, 0)\)-multiplication which is a generalization of the simple \( 0\)- multiplication. It is proved that for arbitrary positive integers \(m\leq n\) and \(n\geq 2\), \(R[x; \sigma]\) is a reduced ring if and only if...
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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/1020 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | Let \(R\) be a ring with an endomorphism \(\sigma\). We introduce \((\overline{\sigma}, 0)\)-multiplication which is a generalization of the simple \( 0\)- multiplication. It is proved that for arbitrary positive integers \(m\leq n\) and \(n\geq 2\), \(R[x; \sigma]\) is a reduced ring if and only if \(S_{n, m}(R)\) is a ring with \((\overline{\sigma},0)\)-multiplication. |
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