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

Author(s): V. Linchenko; S. Montgomery
Journal: Proc. Amer. Math. Soc. 135 (2007), 3091-3098.
MSC (2000): Primary 16W30, 16N20, 16R99, 16S40
Posted: June 20, 2007
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Abstract: Assume that $ H$ is a finite-dimensional Hopf algebra over a field $ k$ and that $ A$ is an $ H$-module algebra satisfying a polynomial identity (PI). We prove that if $ H$ is semisimple and $ A$ is $ H$-semiprime, then $ A\char93 H$ is semiprime. If $ H$ is cosemisimple, we show that the prime radical of $ A$ is $ H$-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: 10.1090/S0002-9939-07-08849-1
PII: S 0002-9939(07)08849-1
Received by editor(s): March 6, 2006
Received by editor(s) in revised form: July 15, 2006
Posted: June 20, 2007
Additional Notes: The second author was supported by NSF grant DMS-0401399.
Communicated by: Martin Lorenz
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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