Coxeter Diagrams and the Köthe's Problem

Abstract

A ring is called right Köthe if every right -module is a direct sum of cyclic modules. In this paper, we give a characterization of basic hereditary right Köthe rings in terms of their Coxeter valued quivers. We also give a characterization of basic right Köthe rings with radical square zero. Therefore, we give a solution to Köthe's problem in these two cases. © Canadian Mathematical Society 2020.