The radicals of Hopf module algebras (Q1377226)

Let \(H\) be a Hopf algebra. \textit{J. R. Fisher} [J. Algebra 34, 217-231 (1975; Zbl 0306.16012)]\ developed a theory of \(H\)-radicals for \(H\)-module algebras. The aim of the present paper is to specialize this theory for the \(H\)-prime radical. Several characterizations are given, and for an \(H\)-module algebra \(A\), the relationship between the prime radical of the smash product \(A\#H\) and the \(H\)-prime radical of \(A\) is described.