Dualizing complexes over noncommutative local rings

DOI10.1006/jabr.2000.8689zbMath1001.16004OpenAlexW2083442773MaRDI QIDQ5942806

James J. Zhang, Quan Shui Wu

Publication date: 30 May 2002

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8689

zbMATH Keywords

dualizing complexeslocal cohomologyAuslander-Buchsbaum formulaBass theoremno-holes theoremNoetherian local algebrasPI algebrassemilocal algebras

Mathematics Subject Classification ID

Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Noncommutative local and semilocal rings, perfect rings (16L30) Syzygies, resolutions, complexes in associative algebras (16E05) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (18)

On Gorenstein projective, injective and flat dimensions -- a functorial description with applications ⋮ Existence of Gorenstein projective resolutions and Tate cohomology ⋮ Ore localization and minimal injective resolutions. ⋮ Calabi–Yau Coalgebras ⋮ Skew Calabi-Yau algebras and homological identities. ⋮ Homological identities for differential graded algebras. ⋮ 𝐴_{∞}-structures associated with pairs of 1-spherical objects and noncommutative orders over curves ⋮ Dualizing Complexes of Noetherian Complete Algebras via Coalgebras ⋮ Homological identities for noncommutative rings ⋮ Symmetry theorems for Ext vanishing ⋮ Weak proregularity, weak stability, and the noncommutative MGM equivalence ⋮ Finite Flat and Projective Dimension ⋮ Prime ideals of \(q\)-commutative power series rings. ⋮ Rings with Auslander dualizing complexes ⋮ Cohen-Macaulay invariant subalgebras of Hopf dense Galois extensions ⋮ Pre-balanced dualizing complexes ⋮ Finite generation for Hochschild cohomology of Gorenstein monomial algebras ⋮ Gorenstein Dimension and AS-Gorenstein Algebras

Cites Work

• Morita duality and Noetherian rings
• Rings with Morita duality
• Dualizing complexes over noncommutative graded algebras
• Rings with Auslander dualizing complexes
• Derived categories and Morita duality theory
• Homological properties of (graded) Noetherian PI rings
• Existence theorems for dualizing complexes over non-commutative graded and filtered rings
• Catenarity in quantum algebras
• Some homological invariants of local PI algebras
• The residue complex of a noncommutative graded algebra
• Local cohomology for non-commutative graded algebras
• A note on three artinian rings
• Two applications of dualizing complexes over local rings
• Semi-Local Noetherian PI -Rings
• Serre duality for noncommutative projective schemes
• Serre-duality for Tails(𝐴)
• The Baire Category Property and Some Notions of Compactness
• Noncommutative rational double points
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