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40 - M. Behboodi (Joint with S. H. Shojaee), Commutative local rings whose ideals are direct sum of cyclic modules, Algebr. Represent Theor. (2013), DOI: 10.1007/s10468-013-9427-x

A well-known result of Köthe and Cohen-Kaplansky states that a commutative ring R has the property that every R-module is a direct sum of cyclic modules if and only if R is an Artinian principal ideal ring. This motivated us to study commutative rings for which every ideal is a direct sum of cyclic modules. Recently, in Behboodi et al. Commutative Noetherian local rings whose ideals are direct sums of cyclic modules (J. Algebra 345:257–265, 2011) the authors considered this question in the context of finite direct products of commutative Noetherian local rings. In this
paper, we continue their study by dropping the Noetherian condition.

Journal Papers
Month/Season: 
January
Year: 
2014