Coxeter diagrams and the Köthe's problem

Abstract

A ring $\Lambda$ is called right Köthe if every right $\Lambda$-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. Also we give a characterization of basic right Köthe rings with radical square zero. Therefore we give a solution of the Köthe's problem in this cases.

arXiv commentto appear in Canad. J. Math