Towards a theory of Bass numbers with application to Gorenstein algebras

DOI10.4064/cm91-2-4zbMath1067.16014OpenAlexW2085330762MaRDI QIDQ2773347

Shiro Goto, Kenji Nishida

Publication date: 21 February 2002

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/cm91-2-4

zbMATH Keywords

Cohen-Macaulay ringslocal ringsBass numbersGorenstein algebrasNoetherian algebrashomological dimensionsnon-commutative ringsinjective resolutionsCousin complexesmodule-finite algebras

Mathematics Subject Classification ID

Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Noncommutative local and semilocal rings, perfect rings (16L30) Syzygies, resolutions, complexes in associative algebras (16E05) Homological dimension in associative algebras (16E10) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items

Derived equivalences and Gorenstein algebras, Flat cotorsion modules over Noether algebras, Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories., Auslander correspondence., Classifications of exact structures and Cohen-Macaulay-finite algebras, Auslander's theorem and \(n\)-isolated singularities, Gorenstein modifications and \mathds{𝑄}-Gorenstein rings, Maximal modifications and Auslander-Reiten duality for non-isolated singularities, Extension groups between atoms and objects in locally noetherian Grothendieck category, Auslander-Gorenstein resolution., Auslander-Reiten conjecture in a dual vein, Remarks on dimensions of triangulated categories, Cohen-Macaulay isolated singularities with a dualizing module., Extension groups between atoms in abelian categories, Cohen–Macaulay Modules and Holonomic Modules Over Filtered Rings, Derived equivalences and Serre duality for Gorenstein algebras., Gorenstein Orders Associated with Modules, Distributive lattices and Auslander regular algebras, Finiteness of Selfinjective Dimension for Noetherian Algebras, The Nakayama functor and its completion for Gorenstein algebras