Hereditary Noetherian prime rings. III: Infinitely generated projective modules

DOI10.1006/jabr.1999.8123zbMath0955.16025OpenAlexW4210374105MaRDI QIDQ1972036

Lawrence S. Levy, J. Chris Robson

Publication date: 13 August 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1999.8123

zbMATH Keywords

direct sumssimple modulesdirect summandsgenusDedekind domainshereditary ordershereditary Noetherian prime ringsHNP ringsinfinitely generated projective modulessimple Artinian classical quotient rings

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Prime and semiprime associative rings (16N60) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. (16E60) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50)

Related Items (6)

Noetherian rings of injective dimension one which are orders in quasi-Frobenius rings. ⋮ When every projective module is a direct sum of finitely generated modules ⋮ Extending and lifting of endomorphisms and automorphisms of modules over non-primitive HNP rings ⋮ Non-finitely generated projective modules over generalized Weyl algebras. ⋮ Hereditary Noetherian prime rings. I: Integrality and simple modules ⋮ Hereditary Noetherian prime rings. II: Finitely generated projective modules

Cites Work

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• Hereditary Noetherian prime rings. II: Finitely generated projective modules
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• Serial rings
• Idealizers and hereditary Noetherian prime rings
• Localization and splitting in hereditary noetherian prime rings
• Big projective modules are free
• Constructions of Hereditary Noetherian Rings and Simple Rings
• K-Theory and Right Ideal Class Groups for HNP Rings
• Hidden Matrices
• Modules Over Dedekind Rings and Valuation Rings

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