The Radicals of Crossed Products
classification
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math.RA
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semiprimealgebracrossedsigmaauthorcocommutativecommutativecosemisimle
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The relations between the radical of crossed product $R #_\sigma H$ 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 $R#_{\sigma}H$ is semiprime.
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