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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| Дата: | 2020 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2020
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/493 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-4932020-07-08T07:13:20Z On a common generalization of symmetric rings and quasi duo rings Subedi, T. Roy, D. symmetric ring, Jacobson radical, $J$-symmetric ring 13C99, 16D80, 16U80 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. Lugansk National Taras Shevchenko University 2020-07-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/493 10.12958/adm493 Algebra and Discrete Mathematics; Vol 29, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/493/pdf Copyright (c) 2020 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
symmetric ring Jacobson radical $J$-symmetric ring 13C99 16D80 16U80 |
| spellingShingle |
symmetric ring Jacobson radical $J$-symmetric ring 13C99 16D80 16U80 Subedi, T. Roy, D. On a common generalization of symmetric rings and quasi duo rings |
| topic_facet |
symmetric ring Jacobson radical $J$-symmetric ring 13C99 16D80 16U80 |
| format |
Article |
| author |
Subedi, T. Roy, D. |
| author_facet |
Subedi, T. Roy, D. |
| author_sort |
Subedi, T. |
| title |
On a common generalization of symmetric rings and quasi duo rings |
| title_short |
On a common generalization of symmetric rings and quasi duo rings |
| title_full |
On a common generalization of symmetric rings and quasi duo rings |
| title_fullStr |
On a common generalization of symmetric rings and quasi duo rings |
| title_full_unstemmed |
On a common generalization of symmetric rings and quasi duo rings |
| title_sort |
on a common generalization of symmetric rings and quasi duo rings |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/493 |
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2024-04-12T06:26:12Z |
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2024-04-12T06:26:12Z |
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