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On modules \(M\) for which \(N\cong M\) for every submodule \(N\) of size \(|M|\)

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Publication:847989
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DOI10.1216/JCA-2009-1-4-679zbMath1184.13031OpenAlexW2039062235MaRDI QIDQ847989

Greg G. Oman

Publication date: 19 February 2010

Published in: Journal of Commutative Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/jca-2009-1-4-679

zbMATH Keywords

isomorphismscongruent modules


Mathematics Subject Classification ID

Structure, classification theorems for modules and ideals in commutative rings (13C05) Ordinal and cardinal numbers (03E10)


Related Items

Elementarily \(\lambda\)-homogeneous binary functions, Strongly Jónsson and strongly HS modules, On elementarily κ-homogeneous unary structures, Modules Which are Isomorphic to Their Factor Modules, Rings whose subrings have an identity



Cites Work

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  • Unnamed Item
  • Modules whose proper submodules are finitely generated
  • Injective modules over Noetherian rings
  • On the number of normal subgroups of an uncountable soluble group
  • On infinite modules \(M\) over a Dedekind domain for which \(N\cong M\) for every submodule \(N\) of cardinality \(|M|\)
  • On Jónsson algebras over a commutative ring
  • On infinite groups
  • An Application of Jonsson Modules to Some Questions Concerning Proper Subrings.
  • Cardinality of generating sets for modules over a commutative ring.
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