Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University453310.18287/2541-7525-2014-20-7-70-74ON VARIETIES OF ASSOCIATIVE ALGEBRAS WITH WEAK GROWTHRatseevS.M.morenov.sv@ssau.ruUlyanovsk State University3011201420770743005201730052017Copyright © 2014, Ratseev S.2014We 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.ассоциативная алгебраалгебра Лимногообразие алгебррост многообразия