The Baer and Jacobson radicals of crossed products

DOI10.1023/A:1006510201612zbMATH Open0909.16020arXivmath/0311530OpenAlexW1775142783MaRDI QIDQ1276273

Shouchuan Zhang

Publication date: 24 January 1999

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

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

Full work available at URL: https://arxiv.org/abs/math/0311530

zbMATH Keywords

Hopf algebrasJacobson radicalmodule algebrasBaer radicalprime radicalsemiprime crossed productssmash products of general Hopf actions

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Twisted and skew group rings, crossed products (16S35) General radicals and associative rings (16N80) Jacobson radical, quasimultiplication (16N20) Smash products of general Hopf actions (16S40)

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