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Algebra and Discrete Mathematics, 2007, Issue 3, Pages 38–45 (Mi adm219)  

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
Bibliographic databases:
Document Type: Article
MSC: 16N40
Language: English
Citation: Svitlana V. Bilun, “On sum of a nilpotent and an ideally finite algebras”, Algebra Discrete Math., 2007, no. 3, 38–45
Citation in format AMSBIB
\Bibitem{Bil07}
\by Svitlana~V.~Bilun
\paper On sum of a~nilpotent and an ideally finite algebras
\jour Algebra Discrete Math.
\yr 2007
\issue 3
\pages 38--45
\mathnet{http://mi.mathnet.ru/adm219}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2421776}
\zmath{https://zbmath.org/?q=an:1164.16008}
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