Simple modules over hereditary Noetherian prime rings

DOI10.1016/0021-8693(79)90210-2zbMath0422.16002OpenAlexW2082467128MaRDI QIDQ1133603

Kenneth R. Goodearl, Robert B. jun. Warfield

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1016/0021-8693(79)90210-2

zbMATH Keywords

simple modulesextension probleminjective hullhereditary Noetherian prime ringsidempotent maximal ideals

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Free, projective, and flat modules and ideals in associative algebras (16D40) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Other classes of modules and ideals in associative algebras (16D80) Divisibility, noncommutative UFDs (16U30) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Centralizing and normalizing extensions (16S20) Representation theory of associative rings and algebras (16Gxx)

Related Items (22)

Ore-Rees rings which are maximal orders. ⋮ Wild torsion modules over Weyl algebras and general torsion modules over HNPs ⋮ Generalized hereditary Noetherian prime rings ⋮ Torsion modules over the ring of differential polynomials ⋮ Examples of Ore extensions which are maximal orders whose based rings are not maximal orders ⋮ Non commutative unique factorization rings ⋮ The number of generators of a module over a fully bounded ring ⋮ State spaces of \(K_ 0\) of Noetherian rings ⋮ Positively graded rings which are maximal orders and generalized Dedekind prime rings ⋮ Hereditary Noetherian prime rings. III: Infinitely generated projective modules ⋮ Positively graded rings which are unique factorization rings ⋮ Reflexive ideals and injective modules over Noetherian v-H orders ⋮ Incompressible critical modules ⋮ Ideal invariance and localization ⋮ On hereditary orders ⋮ Presentations over HNP rings with enough invertible ideals and torsionfree cancellation over neoclassical orders ⋮ Injective modules and representational repleteness ⋮ Hereditary orders with infinitely many idempotent ideals ⋮ Modules ⋮ Hereditary Noetherian prime rings. I: Integrality and simple modules ⋮ Hereditary Noetherian prime rings. II: Finitely generated projective modules ⋮ Gorenstein rings with semigroup bases

Cites Work

• Modules over Dedekind prime rings
• Hereditary Noetherian prime rings
• Ideals and modules of simple Noetherian hereditary rings
• Serial rings
• Idealizers and hereditary Noetherian prime rings
• Localization and splitting in hereditary noetherian prime rings
• Homomorphisms and extensions of modules over certain differential polynomial rings
• Modules Over Hereditary Noetherian Prime Rings, II
• Homological properties of the ring of differential polynomials
• Bounded Hereditary Noetherian Prime Rings

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