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A ring Ris called left k-cyclic if every left R-module is a direct sum of indecomposable modules which are homomorphic image of RRk. In this paper, we give a characterization of left k-cyclic rings. As a consequence, we give a characterization of left KÃ¶the rings, which is a generalization of KÃ¶theï¿½??Cohenï¿½??Kaplansky theorem. We also characterize rings which are Morita equivalent to a basic left k-cyclic ring. As a corollary, we show that Ris Morita equivalent to a basic left KÃ¶the ring if and only if Ris an artinian left multiplicity-free top ring.
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