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A ring R is called right KÂ¨othe if every right R-module is a direct sum of cyclic modules. In this paper, we give a characterization of basic hereditary right KÂ¨othe rings in terms of their Coxeter valued quivers. Also we give a characterization of basic right KÂ¨othe rings with radical square zero. Therefore we give a solution of the KÂ¨otheï¿½??s problem in these two cases.
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