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...
Збережено в:
| Дата: | 2006 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2006
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/157377 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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. |
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