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Connections between Representation-Finite and K\'othe Rings
- Source :
- Journal of Algebra 514 (2018) 25-39
- Publication Year :
- 2017
-
Abstract
- A ring $R$ is called left $k$-cyclic if every left $R$-module is a direct sum of indecomposable modules which are homomorphic image of $_{R}R^k$. In this paper, we give a characterization of left $k$-cyclic rings. As a consequence, we give a characterization of left K\"othe rings, which is a generalization of K\"othe-Cohen-Kaplansky theorem. We also characterize rings which are Morita equivalent to a basic left $k$-cyclic ring. As a corollary, we show that $R$ is Morita equivalent to a basic left K\"othe ring if and only if $R$ is an artinian left multiplicity-free top ring.
- Subjects :
- Mathematics - Rings and Algebras
Mathematics - Representation Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Algebra 514 (2018) 25-39
- Publication Type :
- Report
- Accession number :
- edsarx.1712.03383
- Document Type :
- Working Paper