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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the codimension growth of $ G$-graded algebras


Author: Eli Aljadeff
Journal: Proc. Amer. Math. Soc. 138 (2010), 2311-2320
MSC (2010): Primary 16P90, 16R10, 16W50
Published electronically: March 10, 2010
MathSciNet review: 2607860
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Abstract: Let $ W$ be an associative PI-affine algebra over a field $ F$ of characteristic zero. Suppose $ W$ is $ G$-graded where $ G$ is a finite group. Let $ \exp(W)$ and $ \exp(W_{e})$ denote the codimension growth of $ W$ and of the identity component $ W_{e}$, respectively. We prove $ \exp(W)\leq \vert G\vert^2 \exp(W_{e}).$ This inequality had been conjectured by Bahturin and Zaicev.


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Additional Information

Eli Aljadeff
Affiliation: Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel
Email: aljadeff@tx.technion.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10282-2
PII: S 0002-9939(10)10282-2
Keywords: Graded algebra, polynomial identity
Received by editor(s): August 29, 2009
Received by editor(s) in revised form: November 3, 2009
Published electronically: March 10, 2010
Additional Notes: The author was partially supported by the Israel Science Foundation (grant No. 1283/08) and by the E. Schaver Research Fund
Communicated by: Martin Lorenz
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.