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: | Англійська |
| Опубліковано: |
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 |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543230641831936 |
|---|---|
| author | Abdioglu, Cihat Şahinkaya, Serap KÖR, Arda |
| author_facet | Abdioglu, Cihat Şahinkaya, Serap KÖR, Arda |
| author_sort | Abdioglu, Cihat |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T01:41:11Z |
| 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. |
| first_indexed | 2025-12-02T15:29:16Z |
| format | Article |
| id | admjournalluguniveduua-article-1020 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:29:16Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 |
| title | 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_short | Rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication |
| title_sort | rigid, quasi-rigid and matrix rings with \((\overline{\sigma},0)\)multiplication |
| topic | simple \(0\)-multiplication quasi \(\sigma\)-rigid rings 16N60,16S36,16W60 |
| topic_facet | simple \(0\)-multiplication quasi \(\sigma\)-rigid rings 16N60,16S36,16W60 |
| 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 |