  A ring $\Lambda$ is called right K\"othe if every right $\Lambda$-module is a
direct sum of cyclic modules. In this paper, we give a characterization of
basic hereditary right K\"othe rings in terms of their Coxeter valued quivers.
Also we give a characterization of basic right K\"othe rings with radical
square zero. Therefore we give a solution of the K\"othe's problem in this
cases.
