Geodesic
Varieties of linear algebras with colength one
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2010), pp. 25-30

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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 $x^2x\equiv 0.$ 
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     title = {Varieties of linear algebras with colength one},
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S. P. Mishchenko. Varieties of linear algebras with colength one. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2010), pp. 25-30. http://geodesic.mathdoc.fr/item/VMUMM_2010_1_a3/