Commutative rings whose proper ideals are pure-semisimple

DOI10.1080/00927872.2023.2217720zbMath1527.13011OpenAlexW4379513505MaRDI QIDQ6094265

Ali Moradzadeh-Dehkordi, Samaneh Baghdari, Mahmood Behboodi

Publication date: 10 October 2023

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927872.2023.2217720

zbMATH Keywords

direct sum decompositionArtinian principal ideal ringserial modulepure-semisimple module

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Principal ideal rings (13F10) Structure, classification theorems for modules and ideals in commutative rings (13C05) Local rings and semilocal rings (13H99)

Cites Work

• Commutative Noetherian local rings whose ideals are direct sums of cyclic modules
• Commutative local rings whose ideals are direct sums of cyclic modules
• Rings with the dual of the isomorphism theorem.
• Commutative rings whose proper ideals are serial
• On the decomposition of modules and generalized left uniserial rings
• 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
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