FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 7, PAGES 53-

Regev's and Amitsur's conjectures for codimensions of generalized polynomial identities

A. S. Gordienko

Abstract

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Let $A$ be a finite-dimensional associative algebra over a field of characteristic $0$. Then there exist $C$Î Q₊ and $t$Î Z₊ such that $gc$_n(A) ~ C n^t dⁿ as $n\; \to$¥, where $d\; =\; PIexp(A)$. In particular, Amitsur's and Regev's conjectures hold for the codimensions $gc$_n(A) of generalized polynomial identities.

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Last modified: June 25, 2009