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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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Інститут прикладної математики і механіки НАН України
2006
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/157377 |
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irk-123456789-1573772019-06-21T01:28:15Z On the Amitsur property of radicals Loi, N.V. Wiegandt, R. 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. 2006 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/157377 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Loi, N.V. Wiegandt, R. |
| spellingShingle |
Loi, N.V. Wiegandt, R. On the Amitsur property of radicals Algebra and Discrete Mathematics |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT loinv ontheamitsurpropertyofradicals AT wiegandtr ontheamitsurpropertyofradicals |
| first_indexed |
2023-05-20T17:51:52Z |
| last_indexed |
2023-05-20T17:51:52Z |
| _version_ |
1796154275568549888 |