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“School of Mathematics”

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Paper   IPM / M / 15529
School of Mathematics
  Title:   Connections between representation-finite and Kothe rings
  Author(s): 
1.  Ziba Fazelpour
2.  Alireza Nasr-Isfahani
  Status:   Published
  Journal: J. Algebra
  Vol.:  514
  Year:  2018
  Pages:   25-39
  Supported by:  IPM
  Abstract:
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 Köthe rings, which is a generalization of Köthe�??Cohen�??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 Köthe ring if and only if Ris an artinian left multiplicity-free top ring.

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