The von Neumann regular radical and Jacobson radical of crossed products

DOI10.1023/A:1006723709818zbMATH Open0969.16004arXivmath/0311519OpenAlexW1911987511MaRDI QIDQ5932673

Shouchuan Zhang

Publication date: 12 June 2001

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

Abstract: We construct the $H$-von Neumann regular radical for $H$-module algebras and show that it is an $H$-radical property. We obtain that the Jacobson radical of twisted graded algebra is a graded ideal. For twisted $H$-module algebra $R$, we also show that $$ and the Jacobson radical of $R$ is stable, when $k$ is an algebraically closed field or there exists an algebraic closure $F$ of $k$ such that $r_j(RotimesF)=r_j(R)otimesF$, where $H$ is a finite-dimensional, semisimple, cosemisimple, commutative or cocommutative Hopf algebra over $k$. In particular, we answer two questions J.R.Fisher asked.

Full work available at URL: https://arxiv.org/abs/math/0311519

zbMATH Keywords

crossed productsHopf algebrasJacobson radicalsmash productsvon Neumann regular radical

Mathematics Subject Classification ID

Twisted and skew group rings, crossed products (16S35) General radicals and associative rings (16N80) Jacobson radical, quasimultiplication (16N20)

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