The Von Neumann Regular Radical and Jacobson Radical of Crossed Products

Details The Von Neumann Regular Radical and Jacobson Radical of Crossed Products The Von Neumann Regular Radical and Jacobson Radical of Crossed Products

2003-11-28

arxiv.org/abs/math/0311519v1

Acta Math. Hungar., 86(2000)4, 319-333

Mathematics

Quantum Algebra

15pages

Scientific paper

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 $r_{j}(R#_\sigma H)= r_{Hj}(R)#_\sigma H$ 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 $r_j(R \otimes F) = r_j(R) \otimes F$, 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.

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