Hereditary Noetherian prime rings. I: Integrality and simple modules

DOI10.1006/jabr.1999.7884zbMath0946.16016OpenAlexW1984999890MaRDI QIDQ1306893

J. Chris Robson, Lawrence S. Levy

Publication date: 20 December 1999

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

Full work available at URL: https://doi.org/10.1006/jabr.1999.7884

zbMATH Keywords

projective modulesuniserial modulessimple modulesDedekind domainshereditary ringshereditary Noetherian prime ringsHNP ringsintegral extensionsDedekind closuresGoldie quotient ringsintegral overrings

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) Centralizing and normalizing extensions (16S20)

Related Items (5)

Noetherian rings of injective dimension one which are orders in quasi-Frobenius rings. ⋮ Tilting modules arising from ring epimorphisms. ⋮ Hereditary Noetherian prime rings. III: Infinitely generated projective modules ⋮ Extending and lifting of endomorphisms and automorphisms of modules over non-primitive HNP rings ⋮ Hereditary Noetherian prime rings. II: Finitely generated projective modules

Cites Work

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• Hereditary Noetherian prime rings. III: Infinitely generated projective modules
• Noncommutative localizations and applications
• Modules over Dedekind prime rings
• Hereditary Noetherian prime rings
• Serial rings
• Idealizers and hereditary Noetherian prime rings
• Localization and splitting in hereditary noetherian prime rings
• Constructions of Hereditary Noetherian Rings and Simple Rings
• K-Theory and Right Ideal Class Groups for HNP Rings

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