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Paper   IPM / M / 16887
School of Mathematics
  Title:   Coxeter diagrams and the Kothe 's problem
1.  Ziba Fazelpour
2.  Alireza Nasr-Isfahani
  Status:   Published
  Journal: Canad. J. Math
  Vol.:  73
  Year:  2021
  Pages:   656-686
  Supported by:  IPM
A ring R is called right K¨othe if every right R-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 these two cases.

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