Let V be a variety of non necessarily associative algebras over a field of characteristic zero. The growth of V is determined by the asymptotic behavior of the sequence of codimensions c(n) (V),n = 1,2,..., and here we study varieties of polynomial growth. We classify all possible growth of varieties V of algebras satisfying the identity x(yz) equivalent to 0 such that c(n) (V) < C-n(alpha) with 1 <= alpha < 3, for some constant C. We prove that if 1 <= alpha < 2 then c(n) (V) <= C-1n, and if 2 <= alpha < 3, then c(n)(V) <= C(2)n(2), for some constants C-1, C-2. (C) 2018 Elsevier Inc. All rights reserved.
|Numero di pagine||22|
|Rivista||Journal of Algebra|
|Stato di pubblicazione||Published - 2019|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory