Commutative rings whose proper ideals are direct sum of completely cyclic modules

DOI10.1142/S0219498816501607zbMath1349.13019OpenAlexW2175526021MaRDI QIDQ2816933

S. Roointan-Isfahani, S. Heidari, Mahmood Behboodi

Publication date: 26 August 2016

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498816501607

zbMATH Keywords

cyclic modulesprincipal ideal ringcompletely cyclic moduledirect sum of cyclic

Mathematics Subject Classification ID

Principal ideal rings (13F10) Commutative Noetherian rings and modules (13E05) Structure, classification theorems for modules and ideals in commutative rings (13C05) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Local rings and semilocal rings (13H99)

Related Items (3)

Commutative rings whose proper ideals are serial ⋮ Structure of virtually semisimple modules over commutative rings ⋮ Commutative rings whose proper ideals are direct sums of uniform modules

Cites Work

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• Rings for which every module is a direct sum of cyclic modules
• On left Köthe rings and a generalization of a Köthe-Cohen-Kaplansky theorem
• On commutative rings whose prime ideals are direct sums of cyclics

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