Geodesic
On sum of a~nilpotent and an ideally finite algebras
Algebra and discrete mathematics, no. 3 (2007), pp. 38-45

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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, finite dimensional ideal, left annihilator.
Mots-clés : sum of subalgebras 
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Svitlana V. Bilun. On sum of a~nilpotent and an ideally finite algebras. Algebra and discrete mathematics, no. 3 (2007), pp. 38-45. http://geodesic.mathdoc.fr/item/ADM_2007_3_a5/