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Varieties with at most cubic growth.
- Source :
-
Journal of Algebra . Jan2019, Vol. 518, p321-342. 22p. - Publication Year :
- 2019
-
Abstract
- Abstract 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 (y z) ≡ 0 such that c n (V) < C n α , with 1 ≤ α < 3 , for some constant C. We prove that if 1 ≤ α < 2 then c n (V) ≤ C 1 n , and if 2 ≤ α < 3 , then c n (V) ≤ C 2 n 2 , for some constants C 1 , C 2. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 518
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 133093685
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2018.09.040