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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| Дата: | 2018 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1020 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-10202018-04-26T01:41:11Z Rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication Abdioglu, Cihat Şahinkaya, Serap KÖR, Arda simple \(0\)-multiplication, quasi \(\sigma\)-rigid rings 16N60,16S36,16W60 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. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1020 Algebra and Discrete Mathematics; Vol 17, No 1 (2014) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1020/544 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
simple \(0\)-multiplication quasi \(\sigma\)-rigid rings 16N60,16S36,16W60 |
| spellingShingle |
simple \(0\)-multiplication quasi \(\sigma\)-rigid rings 16N60,16S36,16W60 Abdioglu, Cihat Şahinkaya, Serap KÖR, Arda Rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication |
| topic_facet |
simple \(0\)-multiplication quasi \(\sigma\)-rigid rings 16N60,16S36,16W60 |
| format |
Article |
| author |
Abdioglu, Cihat Şahinkaya, Serap KÖR, Arda |
| author_facet |
Abdioglu, Cihat Şahinkaya, Serap KÖR, Arda |
| author_sort |
Abdioglu, Cihat |
| title |
Rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication |
| title_short |
Rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication |
| title_full |
Rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication |
| title_fullStr |
Rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication |
| title_full_unstemmed |
Rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication |
| title_sort |
rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1020 |
| work_keys_str_mv |
AT abdioglucihat rigidquasirigidandmatrixringswithoverlinesigma0multiplication AT sahinkayaserap rigidquasirigidandmatrixringswithoverlinesigma0multiplication AT korarda rigidquasirigidandmatrixringswithoverlinesigma0multiplication |
| first_indexed |
2024-04-12T06:25:57Z |
| last_indexed |
2024-04-12T06:25:57Z |
| _version_ |
1796109141880602624 |