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Filtered algebraic algebras
Author(s):
Alon
Regev
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1941-1947.
MSC (2010):
Primary 16S15, 16U99
Posted:
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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Additional Information:
Alon
Regev
Affiliation:
Department of Mathematical Sciences, Watson Hall 320, Northern Illinois University, DeKalb, Illinois 60115
Email:
regev@math.niu.edu
DOI:
10.1090/S0002-9939-10-10227-5
PII:
S 0002-9939(10)10227-5
Received by editor(s):
April 24, 2009,
Received by editor(s) in revised form:
August 13, 2009, and September 14, 2009
Posted:
February 9, 2010
Communicated by:
Birge Huisgen-Zimmermann
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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