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Vestnik SamGU. Estestvenno-Nauchnaya Ser., 2014, Issue 7(118), Pages 70–74
(Mi vsgu428)
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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)
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
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
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https://www.mathnet.ru/eng/vsgu428 https://www.mathnet.ru/eng/vsgu/y2014/i7/p70
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Abstract page: | 123 | Full-text PDF : | 36 | References: | 25 |
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