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Varieties of Linear Algebras with Colength One / Mishchenko S.P. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 1. P. 25-30 [Moscow Univ. Math. Bulletin. Vol. 65, No 1, 2010. P. 23-27]. 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 variety of all associative-commutative algebras, the variety of all metabelian Lie algebras, and the variety of soluble Jordan algebras of the step 2 with the identity x2x≡0.
Key words: identities, nonassociative algebras, colength.
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