On partial H-radicals of Jacobson type

Abstract

Let H be a Hopf algebra over a field \(\mathbbm {k}\). In this paper we present a general theory on partial H-radicals in the sense of Amitsur-Kurosh, for partial H-module algebras, as made in Fisher (J Algebra 34:217–231, 1975) and Sidorov (Algebra i Logika 28(6):705–721, 1989) for global actions, and study some partial H-radicals of Jacobson type. Among other results we discuss some questions posed by Fisher (1975) in the context of partial actions.