Tilting modules and Auslander's Gorenstein property.

DOI10.1016/j.jalgebra.2003.12.008zbMath1076.16006OpenAlexW2039670600MaRDI QIDQ1881108

Takayoshi Wakamatsu

Publication date: 4 October 2004

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2003.12.008

zbMATH Keywords

generalized tilting modulesapproximations of modulesAuslander-Gorenstein property

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) 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) Homological dimension in associative algebras (16E10)

Related Items (41)

Homological dimensions relative to preresolving subcategories. II ⋮ Generalized tilting modules with finite injective dimension. ⋮ Selforthogonal modules with finite injective dimension. III. ⋮ A Generalized Version of the Tilting Theorem ⋮ \(k\)-Gorenstein modules. ⋮ Wakamatsu tilting modules with finite injective dimension ⋮ Relative Gorenstein flat modules and dimension ⋮ The abelian closure of an exact category ⋮ When the kernel of a complete hereditary cotorsion pair is the additive closure of a tilting module ⋮ The Auslander-type condition of triangular matrix rings. ⋮ The socle of the last term in a minimal injective resolution. ⋮ Relative syzygies and grade of modules. ⋮ Relative cohomology and generalized Tate cohomology ⋮ On Auslander-type conditions of modules ⋮ On the \(C\)-flatness and injectivity of character modules ⋮ Generalized tilting modules and Frobenius extensions ⋮ ON A DUALITY THEOREM OF WAKAMATSU ⋮ Natural dualities between abelian categories ⋮ ON COHERENCE OF ENDOMORPHISM RINGS ⋮ Cotorsion Theories Involving Auslander and Bass Classes ⋮ Auslander-type conditions and cotorsion pairs. ⋮ Exact categories and infinite tilting ⋮ Coreflexive modules and semidualizing modules with finite projective dimension ⋮ Homological invariants related to semidualizing bimodules ⋮ \(\omega\)-Gorenstein injective modules and dimensions. ⋮ Wakamatsu tilting modules with finite FP-injective dimension ⋮ Relative Gorenstein dimensions ⋮ The homological theory of quasi-resolving subcategories ⋮ Duality pairs induced by one-sided Gorenstein subcategories ⋮ Duality pairs induced by Auslander and Bass classes ⋮ Generalized tilting modules over ring extension ⋮ ∞-costar modules ⋮ k-torsionfree modules with respect to generalized tilting modules ⋮ Exact Krull-Schmidt categories with finitely many indecomposables ⋮ Wakamatsu tilting modules over ring extension ⋮ Relative torsionfree modules with respect to a faithfully balanced bimodule ⋮ Left orthogonal classes of semidualizing bimodules ⋮ Cograde conditions and cotorsion pairs ⋮ Totally reflexive modules with respect to a semidualizing bimodule ⋮ On relative counterpart of Auslander’s conditions ⋮ Wakamatsu tilting pairs

Cites Work

• Stable equivalence for self-injective algebras and a generalization of tilting modules
• Tilting modules of finite projective dimension
• On modules with trivial self-extensions
• Duality for derived categories and cotilting bimodules
• \(k\)-Gorenstein algebras and syzygy modules
• Tilting functors and stable equivalences for selfinjective algebras
• The homological theory of maximal Cohen-Macaulay approximations
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