Almost Lie nilpotent varieties of associative algebras

Abstract

We consider associative algebras over a field. An algebra variety is said to be Lie nilpotent if it satisfies a polynomial identity of the kind [x 1 , x 2 , . . . , x n ] = 0 where [ x 1 , x 2 ] = x 1 x 2 − x 2 x 1 and [x 1 , x 2 By Zorn's Lemma every non-Lie nilpotent variety contains a minimal such variety, called almost Lie nilpotent, as a subvariety. A description of almost Lie nilpotent varieties for algebras over a field of characteristic 0 was made up by Yu.Mal'cev. We find a list of non-prime almost Lie nilpotent varieties of algebras over a field of positive characteristic.