This article is cited in 5 papers

Mathematics

Varieties of linear algebras with colength one

S. P. Mishchenko

Ulyanovsk State University

Abstract: In the case of characteristic zero it is proved that there exist exactly three varieties of linear algebras with the colength equal to one for all degrees. Those are the the variety of all associative-commutative algebras, the variety of all metabelian Lie algebras, and the variety of solube Jordan algebras of the step 2 with the identity $x^2x\equiv 0.$

Key words: identities, nonassociative algebras, colength.

UDC: 512.572

Received: 09.10.2008

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