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} d^{n} 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.

Location: http://mech.math.msu.su/~fpm/eng/k08/k087/k08706h.htm

Last modified: June 25, 2009