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The Radicals of Crossed Products

Shouchuan Zhang
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Abstract

The relations between the radical of crossed product $R #_σH$ and algebra $R$ are obtained. Using this theory, the author shows that if $H$ is a finite-dimensional semisimple, cosemisimle, and either commutative or cocommutative Hopf algebra, then $R$ is $H$-semiprime iff $R$ is semiprime iff $R#_σH$ is semiprime.

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Shouchuan Zhang. 2003-11-28. The Radicals of Crossed Products. https://arxiv.org/abs/math/0311530

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