Geodesic
Almost Lie solvable associative algebra varieties of finite base rank
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 1-6.

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For arbitrary elements $x_1,\ x_2, \ldots$ from an algebra we put $V_1(x_1,x_2) = [x_1,x_2]$ where $[x_1,x_2]=x_1x_2 - x_2x_1$ and define inductively $$V_n(x_1,\ldots, x_{2^n}) = [V_{n-1}(x_1,\ldots x_{2^{n-1}}), V_{n-1}(x_{2^{n-1}+1},\ldots x_{2^n})].$$ An algebra or a variety of algebras is called Lie solvable if it satisfies the identity $V_n(x_1,\ldots, x_{2^n})=0$ for some $n$. Let $F$ be an associative commutative noetherian ring with $1$. In the set of varieties of associative $F$-algebras we find all almost Lie solvable varieties of finite base rank.
Keywords: varieties of associative algebras, PI-algebras.
Mots-clés : Lie solvable algebras 
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O. B. Finogenova. Almost Lie solvable associative algebra varieties of finite base rank. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 1-6. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a0/

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