Geodesic
On varieties of associative algebras with weak growth
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 7 (2014), pp. 70-74 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that any variety of associative algebras with weak growth of the sequence $\{c_n(\mathbf{V})\}_{n\geq 1}$ satisfies the identity $[x_1,x_2][x_3,x_4]\ldots [x_{2s-1},x_{2s}]=0$ for some $s$. As a consequence, the exponent of an arbitrary associative variety with weak growth exists and is an integer and if the characteristic of the ground field is distinct from 2 then there exists no varieties of associative algebras whose growth is intermediate between polynomial and exponential.
Keywords: associative algebra, Lie algebra, variety of algebras, growth of a variety. 
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S. M. Ratseev. On varieties of associative algebras with weak growth. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 7 (2014), pp. 70-74. http://geodesic.mathdoc.fr/item/VSGU_2014_7_a5/

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