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


Filtered algebraic algebras

Author: Alon Regev
Journal: Proc. Amer. Math. Soc. 138 (2010), 1941-1947
MSC (2010): Primary 16S15, 16U99
Published electronically: February 9, 2010
MathSciNet review: 2596027
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Abstract: Small and Zelmanov posed the question whether every element of a graded algebra over an uncountable field must be nilpotent, provided that the homogeneous elements are nilpotent. This question has recently been answered in the negative by Smoktunowicz. In this paper we prove that the answer is affirmative for associated graded algebras of filtered algebraic algebras. Our result is based on Amitsur's theorems on algebras over infinite fields.

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Alon Regev
Affiliation: Department of Mathematical Sciences, Watson Hall 320, Northern Illinois University, DeKalb, Illinois 60115

Received by editor(s): April 24, 2009
Received by editor(s) in revised form: August 13, 2009, and September 14, 2009
Published electronically: February 9, 2010
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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