The von Neumann regular radical and Jacobson radical of crossed products (Q5932673)

Let \(H\) be a Hopf algebra over a commutative unital ring \(K\). For an \(H\)-module algebra \(R\) the notions of the \(H\)-von Neumann radical and the \(H\)-Jacobson radical are studied. The behavior of the latter radical under the smash product construction is examined. In particular, a question raised by \textit{J. R. Fisher} [J. Algebra 34, 217-231 (1975; Zbl 0306.16012)] is answered.