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Algebra and Discrete Mathematics, 2007, Issue 3, Pages 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
Abstract:
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 A2=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.
Keywords:
associative algebra, field, sum of subalgebras, finite dimensional ideal, left annihilator.
Received: 24.09.2007 Revised: 19.02.2008
Citation:
Svitlana V. Bilun, “On sum of a nilpotent and an ideally finite algebras”, Algebra Discrete Math., 2007, no. 3, 38–45
Linking options:
https://www.mathnet.ru/eng/adm219 https://www.mathnet.ru/eng/adm/y2007/i3/p38
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Abstract page: | 132 | Full-text PDF : | 78 | References: | 5 | First page: | 1 |
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