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ON LEFT KÖTHE RINGS AND A GENERALIZATION OF A KÖTHE-COHEN-KAPLANSKY THEOREM.
- Source :
- Proceedings of the American Mathematical Society; Aug2014, Vol. 142 Issue 8, p2625-2631, 7p
- Publication Year :
- 2014
-
Abstract
- In this paper, we obtain a partial solution to the following question of Köthe: For which rings R is it true that every left (or both left and right) R-module is a direct sum of cyclic modules? Let R be a ring in which all idempotents are central. We prove that if R is a left Köthe ring (i.e., every left R-module is a direct sum of cyclic modules), then R is an Artinian principal right ideal ring. Consequently, R is a Köthe ring (i.e., each left and each right R-module is a direct sum of cyclic modules) if and only if R is an Artinian principal ideal ring. This is a generalization of a Köthe-Cohen-Kaplansky theorem. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 142
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 96190426
- Full Text :
- https://doi.org/10.1090/S0002-9939-2014-11158-0