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JOURNALS // Vestnik Samarskogo Universiteta. Estestvenno-Nauchnaya Seriya // Archive

Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014 Issue 7(118), Pages 70–74 (Mi vsgu428)

Mathematics

On varieties of associative algebras with weak growth

S. M. Ratseev

Ulyanovsk State University, Ulyanovsk, 432017, Russian Federation

Abstract: 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.

UDC: 512.572

Received: 03.02.2014
Accepted: 03.02.2014



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