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Algebra and Discrete Mathematics, 2007, выпуск 3, страницы 38–45
(Mi adm219)
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RESEARCH ARTICLE
On sum of a nilpotent and an ideally finite algebras
Svitlana V. Bilun Department of Mechanics and Mathematics, Kiev Taras Shevchenko University, 64, Volodymyrska street, 01033 Kyiv, Ukraine
Аннотация:
We study associative algebras $R$ over arbitrary fields which can be decomposed into a sum $R=A+B$ of their subalgebras $A$ and $B$ such that $A^{2}=0$ and $B$ is ideally finite (is a sum of its finite dimensional ideals). We prove that $R$ has a locally nilpotent ideal $I$ such that $R/I$ is an extension of ideally finite algebra by a nilpotent algebra. Some properties of ideally finite algebras are also established.
Ключевые слова:
associative algebra, field, sum of subalgebras, finite dimensional ideal, left annihilator.
Поступила в редакцию: 24.09.2007 Исправленный вариант: 19.02.2008
Образец цитирования:
Svitlana V. Bilun, “On sum of a nilpotent and an ideally finite algebras”, Algebra Discrete Math., 2007, no. 3, 38–45
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm219 https://www.mathnet.ru/rus/adm/y2007/i3/p38
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Страница аннотации: | 98 | PDF полного текста: | 61 | Первая страница: | 1 |
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