Prime radical of Ore extensions over \(\delta\)-rigid rings
Let R be a ring. Let \(\sigma\) be an automorphism of R and \(\delta\) be a \(\sigma\)-derivation of R. We say that R is a \(\delta\)-rigid ring if \(a\delta(a)\in P(R)\) implies \(a\in P(R)\), \(a \in R\); where P(R) is the prime radical of R. In this article, we find a relation between the prime...
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| Дата: | 2018 |
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| 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/1073 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-10732018-04-04T08:31:48Z Prime radical of Ore extensions over \(\delta\)-rigid rings Bhat, V. K. Radical, automorphism, derivation, completely prime, \(\delta\)-ring, Q-algebra 16-XX; 16P40,16P50,16U20 Let R be a ring. Let \(\sigma\) be an automorphism of R and \(\delta\) be a \(\sigma\)-derivation of R. We say that R is a \(\delta\)-rigid ring if \(a\delta(a)\in P(R)\) implies \(a\in P(R)\), \(a \in R\); where P(R) is the prime radical of R. In this article, we find a relation between the prime radical of a \(\delta\)-rigid ring R and that of \(R[x,\sigma,\delta]\). We generalize the result for a Noetherian Q-algebra (Q is the field of rational numbers). Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1073 Algebra and Discrete Mathematics; Vol 8, No 1 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1073/587 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-04-04T08:31:48Z |
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OJS |
| language |
English |
| topic |
Radical automorphism derivation completely prime \(\delta\)-ring Q-algebra 16-XX 16P40,16P50,16U20 |
| spellingShingle |
Radical automorphism derivation completely prime \(\delta\)-ring Q-algebra 16-XX 16P40,16P50,16U20 Bhat, V. K. Prime radical of Ore extensions over \(\delta\)-rigid rings |
| topic_facet |
Radical automorphism derivation completely prime \(\delta\)-ring Q-algebra 16-XX 16P40,16P50,16U20 |
| format |
Article |
| author |
Bhat, V. K. |
| author_facet |
Bhat, V. K. |
| author_sort |
Bhat, V. K. |
| title |
Prime radical of Ore extensions over \(\delta\)-rigid rings |
| title_short |
Prime radical of Ore extensions over \(\delta\)-rigid rings |
| title_full |
Prime radical of Ore extensions over \(\delta\)-rigid rings |
| title_fullStr |
Prime radical of Ore extensions over \(\delta\)-rigid rings |
| title_full_unstemmed |
Prime radical of Ore extensions over \(\delta\)-rigid rings |
| title_sort |
prime radical of ore extensions over \(\delta\)-rigid rings |
| description |
Let R be a ring. Let \(\sigma\) be an automorphism of R and \(\delta\) be a \(\sigma\)-derivation of R. We say that R is a \(\delta\)-rigid ring if \(a\delta(a)\in P(R)\) implies \(a\in P(R)\), \(a \in R\); where P(R) is the prime radical of R. In this article, we find a relation between the prime radical of a \(\delta\)-rigid ring R and that of \(R[x,\sigma,\delta]\). We generalize the result for a Noetherian Q-algebra (Q is the field of rational numbers). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1073 |
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AT bhatvk primeradicaloforeextensionsoverdeltarigidrings |
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2025-07-17T10:32:17Z |
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2025-07-17T10:32:17Z |
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