Commutative local rings whose ideals are direct sums of cyclic modules

DOI10.1007/s10468-013-9427-xzbMath1300.13009arXiv1201.6076OpenAlexW2963637137MaRDI QIDQ742946

S. H. Shojaee, Mahmood Behboodi

Publication date: 19 September 2014

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.6076

zbMATH Keywords

cyclic modulesdirect sumlocal ring, principal ideal rings

Mathematics Subject Classification ID

Structure, classification theorems for modules and ideals in commutative rings (13C05) Other special types of modules and ideals in commutative rings (13C13) Local rings and semilocal rings (13H99)

Related Items (5)

Commutative rings whose proper ideals are pure-semisimple ⋮ Commutative rings whose proper ideals are serial ⋮ On commutative rings whose ideals are direct sums of cyclic modules ⋮ Commutative rings whose proper ideals are direct sums of uniform modules ⋮ Two criteria to check whether ideals are direct sums of cyclically presented modules

Cites Work

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• Commutative Noetherian local rings whose ideals are direct sums of cyclic modules
• Verallgemeinerte Abelsche Gruppen mit hyperkomplexem Operatorenring
• Commutative rings with restricted minimum condition
• Rings for which every module is a direct sum of cyclic modules
• A Krull-Schmidt Theorem for Infinite Sums of Modules
• Elementary Divisors and Modules

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