ON VARIETIES OF ASSOCIATIVE ALGEBRAS WITH WEAK GROWTH


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Abstract

We prove that any variety of associative algebras with weak growth of the sequence {c_n(V)}_{n\geq 1} satisfies the identity [x_1, x_2][x_3, x_4] . . . [x_2_{s-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.

About the authors

S.M. Ratseev

Ulyanovsk State University

Author for correspondence.
Email: morenov.sv@ssau.ru

References


Copyright (c) 2017 С.М. Рацеев

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