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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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: Let $A=\oplus_{g\in G}A_g$ be a $G$-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 $A_e$ to that of the whole of $A$, 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 $A$ is finite dimensional and $A_e$ 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: http://dx.doi.org/10.1090/S0002-9947-04-03426-9
PII: S 0002-9947(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