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 $A^{2}=0$ 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.

Keywords: associative algebra, field, sum of subalgebras, finite dimensional ideal, left annihilator.

MSC: 16N40

Received: 24.09.2007
Revised: 19.02.2008

Language: English

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