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

2022/08/16 by R. Nikandish, Nikandish, R., M. J. Nikmehr +3
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2208.07942

openalex publication_date 2022/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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