Homological properties of balanced Cohen-Macaulay algebras

DOI10.1090/S0002-9947-02-03166-5zbMath1030.16006OpenAlexW2097209003MaRDI QIDQ4787450

Izuru Mori

Publication date: 7 January 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-02-03166-5

zbMATH Keywords

projective dimensionintersection multiplicitiesArtin-Schelter regular algebrascategories of graded modulesArtin-Schelter Gorenstein algebrasbalanced dualizing complexesFoxby equivalencescohomology functorsCohen-Macaulay approximationsbalanced Cohen-Macaulay algebras

Mathematics Subject Classification ID

Rings arising from noncommutative algebraic geometry (16S38) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Syzygies, resolutions, complexes in associative algebras (16E05) Graded rings and modules (associative rings and algebras) (16W50) Homological dimension in associative algebras (16E10)

Related Items

Cluster tilting modules and noncommutative projective schemes ⋮ Noncommutative Knörrer's periodicity theorem and noncommutative quadric hypersurfaces ⋮ Non-commutative Castelnuovo-Mumford regularity and AS-regular algebras. ⋮ Serre's vanishing conjecture for Ext-groups. ⋮ Asymmetry of Ext-groups ⋮ Finite Flat and Projective Dimension ⋮ Noncommutative graded algebras of finite Cohen-Macaulay representation type ⋮ Gorenstein Dimension and AS-Gorenstein Algebras

Cites Work

• Homological dimensions of unbounded complexes
• Dualizing complexes over noncommutative graded algebras
• Gorenstein homomorphisms of noncommutative rings
• Properties of AS-Cohen-Macaulay algebras
• Noncommutative projective schemes
• Existence theorems for dualizing complexes over non-commutative graded and filtered rings
• Gourmet's guide to Gorensteinness
• Intersection multiplicity over noncommutative algebras
• Local cohomology for non-commutative graded algebras
• The homological theory of maximal Cohen-Macaulay approximations
• Ring Homomorphisms and Finite Gorenstein Dimension

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