Open AccessON VARIETIES OF ASSOCIATIVE ALGEBRAS WITH WEAK GROWTH
Author(s) -
С. М. Рацеев
Publication year - 2014
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2014-20-7-70-74
Subject(s) - associative property , variety (cybernetics) , integer (computer science) , polynomial , mathematics , exponent , exponential function , pure mathematics , sequence (biology) , exponential growth , identity (music) , combinatorics , discrete mathematics , physics , computer science , mathematical analysis , chemistry , linguistics , statistics , philosophy , biochemistry , acoustics , programming language
We prove that any variety of associative algebras with weak growth of the sequence {c_n(V)}_{n\geq 1} satises 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 eld is distinct from 2 then there exists no varieties of associative algebras whose growth is intermediate between polynomial and exponential.