On the semiprime smash product question

Abstract

This is a survey article on a question, posed in 1986 by M.Cohen and D.Fishman, whether the smash product $A\#H$ of a semisimple Hopf algebra and a semiprime left $H$-module algebra $A$ is itself semiprime.

This is a revision of an already published version of this paper. I would like to thank Susan Montgomery for pointing out a severe mistake in referring to a survey article by M.Cohen from 1985 and not to the paper by M.Cohen and D.Fishman from 1986 where the central problem of this paper had been originally addressed. I also would like to thank her for the reference of the Kac-Paljutkin paper

References in corpus (3)

• When is a smash product semiprime?
• A central closure construction for certain extensions. Applications to Hopf algebra actions
• Simple Hopf algebras and deformations of finite groups

Cited by in corpus (1)

• On the notion of 'retractable modules' in the context of algebras