Identities of graded algebras and codimension growth

Authors:
Yu. A. Bahturin and M. V. Zaicev

Translated by:

Journal:
Trans. Amer. Math. Soc. **356** (2004), 3939-3950

MSC (2000):
Primary 16R10, 16W50

Published electronically:
January 16, 2004

MathSciNet review:
2058512

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a -graded associative algebra over a field of characteristic zero. In this paper we develop a conjecture that relates the exponent of the growth of polynomial identities of the identity component to that of the whole of , in the case where the support of the grading is finite. We prove the conjecture in several natural cases, one of them being the case where is finite dimensional and has polynomial growth.

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Additional Information

**Yu. A. Bahturin**

Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1A 5K9 – and – Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia

Email:
yuri@math.mun.ca

**M. V. Zaicev**

Affiliation:
Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia

Email:
zaicev@mech.math.msu.su

DOI:
https://doi.org/10.1090/S0002-9947-04-03426-9

Received by editor(s):
March 6, 2002

Received by editor(s) in revised form:
May 29, 2003

Published electronically:
January 16, 2004

Additional Notes:
The first author was partially supported by MUN Dean of Science Research Grant #38647

The second author was partially supported by RFBR, grants 99-01-00233 and 00-15-96128

Article copyright:
© Copyright 2004
American Mathematical Society