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 γ has the Amitsur property if and only if its semisimple class is polynomially extensible and satisfies: f(x) ∈ γ(A[x]) implies f(0) ∈ γ(A[x]). Applying this criterion, i...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2006 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/157377 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the Amitsur property of radicals / N.V. Loi, R. Wiegandt // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 3. — С. 92–100. — Бібліогр.: 9 назв. — англ. |
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Loi, N.V. Wiegandt, R. 2019-06-20T03:08:45Z 2019-06-20T03:08:45Z 2006 On the Amitsur property of radicals / N.V. Loi, R. Wiegandt // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 3. — С. 92–100. — Бібліогр.: 9 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 16N60. https://nasplib.isofts.kiev.ua/handle/123456789/157377 The Amitsur property of a radical says that the radical of a polynomial ring is again a polynomial ring. A hereditary radical γ has the Amitsur property if and only if its semisimple class is polynomially extensible and satisfies: f(x) ∈ γ(A[x]) implies f(0) ∈ γ(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. Research supported by the Hungarian OTKA Grant # T043034 en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the Amitsur property of radicals Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On the Amitsur property of radicals |
| spellingShingle |
On the Amitsur property of radicals Loi, N.V. Wiegandt, R. |
| 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 |
| author |
Loi, N.V. Wiegandt, R. |
| author_facet |
Loi, N.V. Wiegandt, R. |
| publishDate |
2006 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
The Amitsur property of a radical says that
the radical of a polynomial ring is again a polynomial ring. A
hereditary radical γ has the Amitsur property if and only if its
semisimple class is polynomially extensible and satisfies: f(x) ∈
γ(A[x]) implies f(0) ∈ γ(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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/157377 |
| citation_txt |
On the Amitsur property of radicals / N.V. Loi, R. Wiegandt // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 3. — С. 92–100. — Бібліогр.: 9 назв. — англ. |
| work_keys_str_mv |
AT loinv ontheamitsurpropertyofradicals AT wiegandtr ontheamitsurpropertyofradicals |
| first_indexed |
2025-12-07T16:43:07Z |
| last_indexed |
2025-12-07T16:43:07Z |
| _version_ |
1850868537657131008 |