Krull and Global Dimensions of Semiprime Noetherian PI-Rings

DOI10.2307/1999509zbMath0495.16008OpenAlexW4239044680MaRDI QIDQ3958606

Richard Resco, Lance W. Small, J. Toby Stafford

Publication date: 1982

Full work available at URL: https://doi.org/10.2307/1999509

zbMATH Keywords

finitely generated moduleslocalizationJacobson ringright Krull dimensionright global dimensionheight one primesright noetherian PI-ringssemiprime noetherian PI-ring

Mathematics Subject Classification ID

Homological dimension in associative algebras (16E10) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50) Rings with polynomial identity (16Rxx) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (13)

The principal ideal theorem in prime Noetherian rings ⋮ Ideal arithmetic in Noetherian PI rings ⋮ Sklyanin algebras and Hilbert schemes of points ⋮ Krull Versus Global Dimension in Noetherian P.I. Rings ⋮ The Global Dimension of FBN Rings with enough Clans ⋮ Finitistic dimensions of Noetherian rings ⋮ Localization, completion and the AR property in Noetherian P.I. rings ⋮ Unnamed Item ⋮ Prime ideals in skew polynomial rings and quantized Weyl algebras ⋮ Embedding Differential and Skew Polynomial Rings into Artinian Rings ⋮ Krull and Global Dimensions of Fully Bounded Noetherian Rings ⋮ On the Global Dimension of a Ring Modulo its Nilpotent Radical ⋮ Quantum polynomial algebras

Cites Work

• Prime ideals in PI-rings
• R Noetherian implies \(R\langle X\rangle\) is a Hilbert ring
• The ring \(R<X>\)
• Serre's conjecture
• Non-commutative affine P. I. rings are catenary
• Examples of orders over discrete valuation rings
• A counter-example in ring theory and homological algebra
• On the global dimension of skew polynomial rings - An Addendum
• Localization in PI-rings
• Skew polynomial rings over orders in Artinian rings
• Idealizers and hereditary Noetherian prime rings
• Homological dimensions of some p.i.rings
• Liberal Extensions
• A Change of Rings Theorem
• Global Dimension of Differential Operator Rings
• Krull dimension
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