On the Amitsur property of radicals
The Amitsur property of a radical says that the radical of a polynomial ring is again a polynomial ring. A hereditary radical \(\gamma\) has the Amitsur property if and only if its semisimple class is polynomially extensible and satisfies: \(f(x) \in \gamma(A[x])\) implies \(f(0) \in \gamma(A[x])\)....
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/900 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-9002018-03-21T07:07:28Z On the Amitsur property of radicals Loi, N. V. Wiegandt, R. Amitsur property, hereditary, normal and generalized nil radical 16N60 The Amitsur property of a radical says that the radical of a polynomial ring is again a polynomial ring. A hereditary radical \(\gamma\) has the Amitsur property if and only if its semisimple class is polynomially extensible and satisfies: \(f(x) \in \gamma(A[x])\) implies \(f(0) \in \gamma(A[x])\). Applying this criterion, it is proved that the generalized nil radical has the Amitsur property. In this way the Amitsur property of a not necessarily hereditary normal radical can be checked. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/900 Algebra and Discrete Mathematics; Vol 5, No 3 (2006) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/900/429 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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2018-03-21T07:07:28Z |
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OJS |
| language |
English |
| topic |
Amitsur property hereditary normal and generalized nil radical 16N60 |
| spellingShingle |
Amitsur property hereditary normal and generalized nil radical 16N60 Loi, N. V. Wiegandt, R. On the Amitsur property of radicals |
| topic_facet |
Amitsur property hereditary normal and generalized nil radical 16N60 |
| format |
Article |
| author |
Loi, N. V. Wiegandt, R. |
| author_facet |
Loi, N. V. Wiegandt, R. |
| author_sort |
Loi, N. V. |
| title |
On the Amitsur property of radicals |
| title_short |
On the Amitsur property of radicals |
| title_full |
On the Amitsur property of radicals |
| title_fullStr |
On the Amitsur property of radicals |
| title_full_unstemmed |
On the Amitsur property of radicals |
| title_sort |
on the amitsur property of radicals |
| description |
The Amitsur property of a radical says that the radical of a polynomial ring is again a polynomial ring. A hereditary radical \(\gamma\) has the Amitsur property if and only if its semisimple class is polynomially extensible and satisfies: \(f(x) \in \gamma(A[x])\) implies \(f(0) \in \gamma(A[x])\). Applying this criterion, it is proved that the generalized nil radical has the Amitsur property. In this way the Amitsur property of a not necessarily hereditary normal radical can be checked. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/900 |
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