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Vestnik SamGU. Estestvenno-Nauchnaya Ser., 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 (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
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.
Received: 03.02.2014
Accepted: 03.02.2014
Document Type: Article
UDC: 512.572
Language: Russian
Citation: S. M. Ratseev, “On varieties of associative algebras with weak growth”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014, no. 7(118), 70–74
Citation in format AMSBIB
\Bibitem{Rat14}
\by S.~M.~Ratseev
\paper On varieties of associative algebras with weak growth
\jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya
\yr 2014
\issue 7(118)
\pages 70--74
\mathnet{http://mi.mathnet.ru/vsgu428}
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    Вестник Самарского государственного университета. Естественнонаучная серия
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