On left Köthe rings and a generalization of a Köthe-Cohen-Kaplansky theorem

DOI10.1090/S0002-9939-2014-11158-0zbMath1315.16008OpenAlexW2069930660MaRDI QIDQ3189568

Ali Moradzadeh-Dehkordi, S. H. Shojaee, Atefeh Ghorbani, Mahmood Behboodi

Publication date: 12 September 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2014-11158-0

zbMATH Keywords

direct sums of cyclic modulesleft Köthe ringsArtinian principal ideal ringsright Köthe rings

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) Generalizations of commutativity (associative rings and algebras) (16U80) Artinian rings and modules (associative rings and algebras) (16P20)

Related Items (24)

\textit{RD}-flatness and \textit{RD}-injectivity of simple modules ⋮ Rings whose cyclic modules are pure-injective or pure-projective ⋮ On rings whose modules have nonzero homomorphisms to nonzero submodules. ⋮ On the structure of pure-projective modules and some applications ⋮ Virtually semisimple modules and a generalization of the Wedderburn-Artin theorem ⋮ Local rings whose modules are almost serial ⋮ Rings all of whose prime serial modules are serial ⋮ Pure semisimple and Köthe group rings ⋮ Almost uniserial rings and modules. ⋮ Left co-Köthe rings and their characterizations ⋮ Commutative rings whose proper ideals are pure-semisimple ⋮ Commutative Noetherian local rings whose ideals are direct sums of cyclic modules ⋮ Several characterizations of left Köthe rings ⋮ Infinite-dimensional triangularization ⋮ Several generalizations of the Wedderburn-Artin theorem with applications ⋮ Noetherian rings whose modules are prime serial ⋮ Virtually homo-uniserial modules and rings ⋮ Connections between representation-finite and Köthe rings ⋮ Virtually uniserial modules and rings ⋮ Rings whose (proper) cyclic modules have cyclic automorphism-invariant hulls ⋮ Commutative rings whose proper ideals are direct sum of completely cyclic modules ⋮ Rings whose injective hulls are dual square free ⋮ Prime virtually semisimple modules and rings ⋮ Coxeter Diagrams and the Köthe’s Problem

Cites Work

• Rings with the dual of the isomorphism theorem.
• Verallgemeinerte Abelsche Gruppen mit hyperkomplexem Operatorenring
• On Köthe rings
• On the decomposition of modules and generalized left uniserial rings
• Rings whose modules have nice decompositions
• Rings for which every module is a direct sum of cyclic modules
• Direct Products of Modules
• Rings whose Right Modules are Direct Sums of Indecomposable Modules
• On Rings whose Left Modules are Direct Sums of Finitely Generated Modules
• Note on uni-serial and generalized uni-serial rings
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