Semiprime smash products and stable prime radicals for PIalgebras
Authors:
V. Linchenko and S. Montgomery
Journal:
Proc. Amer. Math. Soc. 135 (2007), 30913098
MSC (2000):
Primary 16W30, 16N20, 16R99, 16S40
Published electronically:
June 20, 2007
MathSciNet review:
2322738
Fulltext PDF Free Access
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Additional Information
Abstract: Assume that is a finitedimensional Hopf algebra over a field and that is an module algebra satisfying a polynomial identity (PI). We prove that if is semisimple and is semiprime, then is semiprime. If is cosemisimple, we show that the prime radical of is stable.
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 S. A. Amitsur, A generalization of Hilbert's Nullstellensatz, AMS Proceedings 8 (1957), 649656. MR 0087644 (19:384a)
 [B]
 G. M. Bergman, On Jacobson radicals of graded rings, preprint, UC Berkeley, 1975.
 [Br]
 A. Braun, Hopf algebra versions of some classical finite group action theorems, preprint (1991, revised 2005).
 [CF]
 M. Cohen and D. Fischman, Hopf Algebras Actions, J. Algebra 100 (1986), 363379. MR 840582 (87i:16012)
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 M. Cohen and S. Montgomery, Group graded rings, smash products, and group actions, AMS Transactions 282 (1984), 237258; Addendum AMS Transactions 300 (1987), 810811. MR 728711 (85i:16002)
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 P. Etingof and S. Gelaki, On finitedimensional semisimple and cosemisimple Hopf algebras in prime charactersistic, Inter. Math. Research Notices 16 (1998), 851864. MR 1643702 (99i:16068)
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 I. N. Herstein, Noncommutative Rings, 2nd Edition, MAA, 1996.
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 N. Jacobson, Structure of Rings, revised edition, AMS Colloquium Publications vol 37, 1964. MR 0222106 (36:5158)
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 R. G. Larson, Characters of Hopf algebras, J. Algebra 17 (1971), 352368. MR 0283054 (44:287)
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 R. G. Larson and D. Radford, Semisimple cosemisimple Hopf algebras, Amer. J. Math. 110 (1988), 187195. MR 926744 (89a:16011)
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 S. Skryabin and F. van Oystaeyen, The Goldie theorem for semiprime algebras, J. Algebra 305 (2006), 292320.
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Additional Information
V. Linchenko
Affiliation:
Yerakhtur, Shilovsky District, Ryazansky Region, Russia 391534
Email:
linchenk@mail.ru
S. Montgomery
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, California 900891113
Email:
smontgom@math.usc.edu
DOI:
http://dx.doi.org/10.1090/S0002993907088491
PII:
S 00029939(07)088491
Received by editor(s):
March 6, 2006
Received by editor(s) in revised form:
July 15, 2006
Published electronically:
June 20, 2007
Additional Notes:
The second author was supported by NSF grant DMS0401399.
Communicated by:
Martin Lorenz
Article copyright:
© Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
