Symmetry and duality on \(n\)-Gorenstein rings.

DOI10.1016/S0021-8693(03)00419-8zbMath1034.16017MaRDI QIDQ1414673

Osamu Iyama

Publication date: 4 December 2003

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

zbMATH Keywords

dualitiessimple modulesNoetherian ringsGorenstein ringsinjective resolutionsflat dimensiondominant numbers

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Representations of associative Artinian rings (16G10) Syzygies, resolutions, complexes in associative algebras (16E05) Homological dimension in associative algebras (16E10) Noetherian rings and modules (associative rings and algebras) (16P40)

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Higher Auslander correspondence for dualizing \(R\)-varieties ⋮ Simple modules over Auslander regular rings ⋮ The existence of maximal \(n\)-orthogonal subcategories. ⋮ Cluster tilting for tilted algebras. ⋮ The relationship between homological properties and representation theoretic realization of artin algebras ⋮ Auslander correspondence. ⋮ Cluster tilting for higher Auslander algebras. ⋮ Artin-Schelter regular algebras and categories. ⋮ The Auslander-type condition of triangular matrix rings. ⋮ Stable categories of spherical modules and torsionfree modules ⋮ On Auslander-type conditions of modules ⋮ Some homological properties of category \(\mathcal{O}\). VI ⋮ Auslander-type conditions and cotorsion pairs. ⋮ \(\tau\)-rigid modules over Auslander algebras ⋮ Higher Auslander algebras admitting trivial maximal orthogonal subcategories. ⋮ Two filtration results for modules with applications to the Auslander condition ⋮ Cohen–Macaulay Modules and Holonomic Modules Over Filtered Rings ⋮ Distributive lattices and Auslander regular algebras

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