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arXiv · 2208.07942

Commutative rings whose proper ideals are direct sum of cyclically presented modules

R. Nikandish·M. J. Nikmehr·A. Yassine
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Abstract

A famous result due to I. M. Isaacs states that if a commutative ring $R$ has the property that every prime ideal is principal, then every ideal of $R$ is principal. This motivates ring theorists to study commutative rings for which every ideal is a direct sum of cyclically presented modules. In this paper, we study commutative rings whose ideals are direct sum of cyclically presented modules.

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R. Nikandish, M. J. Nikmehr, A. Yassine. 2022-08-16. Commutative rings whose proper ideals are direct sum of cyclically presented modules. https://arxiv.org/abs/2208.07942

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