Constructions of Hereditary Noetherian Rings and Simple Rings

DOI10.1112/plms/s3-51.1.1zbMath0573.16007OpenAlexW1983097342MaRDI QIDQ3691875

J. Toby Stafford, Robert B. jun. Warfield

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1112/plms/s3-51.1.1

zbMATH Keywords

global dimensionGoldie dimension\(K_ 0\)hereditary noetherian prime ringsidempotent maximal idealsHNP ringsimple noetherian domainsimple noetherian ringsnoetherian rings of Krull dimension one

Mathematics Subject Classification ID

Grothendieck groups, (K)-theory, etc. (16E20) Infinite-dimensional simple rings (except as in 16Kxx) (16D30) Divisibility, noncommutative UFDs (16U30) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (10)

Hereditary arithmetics ⋮ Simplicity of noncommutative Dedekind domains ⋮ On rings whose finitely generated faithful modules are generators ⋮ An ideal1zer with respect to a link between maximal ideals ⋮ Hereditary Noetherian prime rings. III: Infinitely generated projective modules ⋮ Hereditary orders with infinitely many idempotent ideals ⋮ Hereditary Noetherian prime rings. I: Integrality and simple modules ⋮ Hereditary Noetherian prime rings. II: Finitely generated projective modules ⋮ Bijective 1-cocycles, braces, and non-commutative prime factorization ⋮ Hereditary rings integral over their centers

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