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This article is cited in 1 scientific paper (total in 1 paper)
Mathematical logic, algebra and number theory
Almost Lie solvable associative algebra varieties of finite base rank
O. B. Finogenova Ural State University, Ekaterinburg
Abstract:
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, Lie solvable algebras, PI-algebras.
Received December 6, 2014, published January 21, 2015
Citation:
O. B. Finogenova, “Almost Lie solvable associative algebra varieties of finite base rank”, Sib. Èlektron. Mat. Izv., 12 (2015), 1–6
Linking options:
https://www.mathnet.ru/eng/semr564 https://www.mathnet.ru/eng/semr/v12/p1
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