Kostia Beidar's contribution to module and ring theory

Abstract

At the beginning of his mathematical career Kostia Beidar was working on rings with polynomial identities and primeness conditions for rings. By Posner's theorem the two-sided quotient ring of a prime PI-ring is a finite matrix ring over some field. This result was extended by Martindale to rings with generalised polynomial identities by the construction of the central closure of a prime ring. Kostia was working extensively in this setting and made crucial contributions to the understanding of the theory. While his contribution to general PI theory will be outlined elsewhere we want to sketch here his work on prime rings and the resulting study of (strongly) prime modules. An account on his papers on Hopf algebras is given and attention is drawn to some more recent constructions which grew out from Kostia's basic contributions to this field.