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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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/900 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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