The Von Neumann Regular Radical and Jacobson Radical of Crossed Products

الأصل · EN

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 rⱼ(R#σH)= rHj(R)#σH 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 rⱼ(R ⊗ F) = rⱼ(R) ⊗ 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.