Injective resolutions of Noetherian rings and cogenerators

DOI10.1090/S0002-9939-00-05305-3zbMath0981.16005OpenAlexW1561528821WikidataQ114094109 ScholiaQ114094109MaRDI QIDQ4955818

Jun-Ichi Miyachi

Publication date: 22 May 2000

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-00-05305-3

zbMATH Keywords

projective dimensionderived categoriescategories of modulesinjective cogeneratorsexact sequencesNoetherian ringsinjective hullsflat dimensionAuslander conditioninjective resolutions of complexes

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Module categories in associative algebras (16D90) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Resolutions; derived functors (category-theoretic aspects) (18G10) Syzygies, resolutions, complexes in associative algebras (16E05) Homological dimension in associative algebras (16E10) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (18)

Zaks' lemma for coherent rings. ⋮ Auslander correspondence. ⋮ Semi-tilting modules and mutation. ⋮ Homological behavior of Auslander's \(k\)-Gorenstein rings. ⋮ The Auslander-type condition of triangular matrix rings. ⋮ Algebras with finite relative dominant dimension and almost \(n\)-precluster tilting modules ⋮ On Auslander-type conditions of modules ⋮ Symmetry and duality on \(n\)-Gorenstein rings. ⋮ New Characterizations of Dualizing Modules ⋮ Dominant dimensions, derived equivalences and tilting modules ⋮ Auslander-type conditions and cotorsion pairs. ⋮ Homological invariants related to semidualizing bimodules ⋮ t-structures and cotilting modules over commutative Noetherian rings ⋮ Abelian quotients of triangulated categories ⋮ Tilting modules and Gorenstein rings ⋮ Recollement of homotopy categories and Cohen-Macaulay modules ⋮ Distributive lattices and Auslander regular algebras ⋮ Minimal injective resolutions and Auslander-Gorenstein property for path algebras

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