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arXiv · 1812.06642

Coxeter diagrams and the K\"othe's problem

Ziba Fazelpour·Alireza Nasr-Isfahani
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Abstract

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.

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Ziba Fazelpour, Alireza Nasr-Isfahani. 2018-12-17. Coxeter diagrams and the K\"othe's problem. https://doi.org/10.4153/s0008414x20000115

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