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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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | 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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Algebra and Discrete Mathematics| _version_ | 1856543276836847616 |
|---|---|
| author | Loi, N. V. Wiegandt, R. |
| author_facet | Loi, N. V. Wiegandt, R. |
| author_sort | Loi, N. V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T07:07:28Z |
| 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. |
| first_indexed | 2026-02-08T08:00:39Z |
| format | Article |
| id | admjournalluguniveduua-article-900 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:00:39Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | Amitsur property hereditary normal and generalized nil radical 16N60 Loi, N. V. Wiegandt, R. On the Amitsur property of radicals |
| title | 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_short | On the Amitsur property of radicals |
| title_sort | on the amitsur property of radicals |
| topic | Amitsur property hereditary normal and generalized nil radical 16N60 |
| topic_facet | Amitsur property hereditary normal and generalized nil radical 16N60 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/900 |
| work_keys_str_mv | AT loinv ontheamitsurpropertyofradicals AT wiegandtr ontheamitsurpropertyofradicals |