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Commutative Local Rings Whose Ideals are Direct Sums of Cyclic Modules

Research paper by M. Behboodi, S. H. Shojaee

Indexed on: 07 Jun '13Published on: 07 Jun '13Published in: Algebras and Representation Theory



Abstract

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.