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
Hauptverfasser: Loi, N. V., Wiegandt, R.
Format: Artikel
Sprache:Englisch
Veröffentlicht: 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
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author Loi, N. V.
Wiegandt, R.
author_facet Loi, N. V.
Wiegandt, R.
author_sort Loi, N. V.
baseUrl_str
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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.
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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
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