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

Linchenko, V.; Montgomery, S.

doi:10.1090/S0002-9939-07-08849-1

Semiprime smash products and $H$-stable prime radicals for PI-algebras
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by V. Linchenko and S. Montgomery

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

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

Published electronically: 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 $A\# H$ is semiprime. If $H$ is cosemisimple, we show that the prime radical of $A$ is $H$-stable.

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