Semiprime smash products and -stable prime radicals for PI-algebras

Authors:
V. Linchenko and S. Montgomery

Journal:
Proc. Amer. Math. Soc. **135** (2007), 3091-3098

MSC (2000):
Primary 16W30, 16N20, 16R99, 16S40

DOI:
https://doi.org/10.1090/S0002-9939-07-08849-1

Published electronically:
June 20, 2007

MathSciNet review:
2322738

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Abstract: Assume that is a finite-dimensional 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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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 90089-1113

Email:
smontgom@math.usc.edu

DOI:
https://doi.org/10.1090/S0002-9939-07-08849-1

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 DMS-0401399.

Communicated by:
Martin Lorenz

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.