Geodesic
Coxeter Diagrams and the Köthe’s Problem
Canadian journal of mathematics, Tome 73 (2021) no. 3, pp. 656-686

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DOI

A ring $\unicode[STIX]{x1D6EC}$ is called right Köthe if every right $\unicode[STIX]{x1D6EC}$-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.
DOI : 10.4153/S0008414X20000115
Mots-clés : right Köthe ring, representation-finite ring, species, partial Coxeter functor, Coxeter functor, Coxeter valued quiver, separated diagram 
Fazelpour, Ziba; Nasr-Isfahani, Alireza. Coxeter Diagrams and the Köthe’s Problem. Canadian journal of mathematics, Tome 73 (2021) no. 3, pp. 656-686. doi: 10.4153/S0008414X20000115
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     author = {Fazelpour, Ziba and Nasr-Isfahani, Alireza},
     title = {Coxeter {Diagrams} and the {K\"othe{\textquoteright}s} {Problem}},
     journal = {Canadian journal of mathematics},
     pages = {656--686},
     year = {2021},
     volume = {73},
     number = {3},
     doi = {10.4153/S0008414X20000115},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X20000115/}
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