On a common generalization of symmetric rings and quasi duo rings
Let \(J(R)\) denote the Jacobson radical of a ring \(R\). We call a ring \(R\) as \(J\)-symmetric if for any \(a,b, c\in R, abc=0\) implies \(bac\in J(R)\). It turns out that \(J\)-symmetric rings are a common generalization of left (right) quasi-duo rings and generalized weakly symmetric rings. Va...
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| Datum: | 2020 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2020
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/493 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | Let \(J(R)\) denote the Jacobson radical of a ring \(R\). We call a ring \(R\) as \(J\)-symmetric if for any \(a,b, c\in R, abc=0\) implies \(bac\in J(R)\). It turns out that \(J\)-symmetric rings are a common generalization of left (right) quasi-duo rings and generalized weakly symmetric rings. Various properties of these rings are established and some results on exchange rings and the regularity of left SF-rings are generalized. |
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