Comparison of relative cohomology theories with respect to semidualizing modules

DOI10.1007/s00209-009-0480-4zbMath1190.13007arXiv0706.3635OpenAlexW2132180373MaRDI QIDQ848828

Tirdad Sharif, Diana White, Sean K. Sather-Wagstaff

Publication date: 23 February 2010

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.3635

zbMATH Keywords

Bass classrelative homological algebrabalancerelative cohomologysemidualizingGorenstein homological dimensionsAuslander classsemi-dualizing

Mathematics Subject Classification ID

Syzygies, resolutions, complexes and commutative rings (13D02) Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07)

Related Items (39)

Notes on linkage of modules with respect to a semidualizing module ⋮ Relative tor functors for level modules with respect to a semidualizing bimodule ⋮ Cotorsion pairs induced by duality pairs ⋮ Relative weak injective and weak flat modules with respect to a semidualizing module ⋮ A study of Tate homology via the approximation theory with applications to the depth formula ⋮ Tate cohomology with respect to semidualizing modules ⋮ The balance of relative Ext groups defined by semidualizing modules ⋮ AB-contexts and stability for Gorenstein flat modules with respect to semidualizing modules ⋮ Balance for relative cohomology of complexes ⋮ Relative grade and relative Gorenstein dimension with respect to a semidualizing module ⋮ Gorenstein projective dimension with respect to a semidualizing module ⋮ Gorenstein \(FI\)-flat dimension and relative homology ⋮ Preservation of quasi-isomorphisms of complexes ⋮ On reduced G-perfection and horizontal linkage ⋮ Remarks on balance for Tate and generalized Tate (co)homology ⋮ Relative cohomology and generalized Tate cohomology ⋮ A model structure approach to the Tate-Vogel cohomology ⋮ Relative cohomology of complexes ⋮ Syzygy and torsionless modules with respect to a semidualizing module ⋮ Gorenstein cohomology of N-complexes ⋮ New Characterizations of Dualizing Modules ⋮ Relative cohomology of complexes based on cotorsion pairs ⋮ Tate homology of modules based on Tate \(\mathcal {F}_C\)-resolutions ⋮ Duality pairs induced by Gorenstein projective modules with respect to semidualizing modules ⋮ Cotorsion Theories Involving Auslander and Bass Classes ⋮ Complete intersection dimensions and Foxby classes ⋮ Gorenstein Homological Dimensions of Complexes with Respect to a Semidualizing Module ⋮ Gorenstein Right Derived Functors of − ⊗ −with Respect to Semidualizing Modules ⋮ Relative tor functors with respect to a semidualizing module ⋮ When every pure ideal is projective ⋮ On Balance for Relative Homology ⋮ Relative tilting modules with respect to a semidualizing module ⋮ Generalized tilting modules over ring extension ⋮ Wakamatsu tilting modules over ring extension ⋮ Relative torsionfree modules with respect to a faithfully balanced bimodule ⋮ Balance for relative (co)homology in abelian categories ⋮ WEAK AB-CONTEXT FOR FP-INJECTIVE MODULES WITH RESPECT TO SEMIDUALIZING MODULES ⋮ Totally reflexive modules with respect to a semidualizing bimodule ⋮ Relative and Tate homology with respect to semidualizing modules

Cites Work

• Unnamed Item
• Unnamed Item
• Gorenstein projective dimension with respect to a semidualizing module
• Homological invariants associated to semi-dualizing bimodules.
• Semi-dualizing modules and related Gorenstein homological dimensions
• Existence of Gorenstein projective resolutions and Tate cohomology
• The set of semidualizing complexes is a nontrivial metric space
• Gorenstein homological dimensions and Auslander categories
• Foxby equivalence over associative rings.
• Gorenstein homological dimensions.
• Gorenstein dimensions
• Gorenstein injective and projective modules
• Relative homological algebra
• Semidualizing modules and the divisor class group
• Extensions of a dualizing complex by its ring: Commutative versions of a conjecture of Tachikawa
• Semi-dualizing complexes and their Auslander categories
• ABSOLUTE, RELATIVE, AND TATE COHOMOLOGY OF MODULES OF FINITE GORENSTEIN DIMENSION
• Gorenstein Modules and Related Modules.
• Classes of extensions and resolutions
• Reflexivity and Ring Homomorphisms of Finite Flat Dimension
• The homological theory of maximal Cohen-Macaulay approximations
• Ring Homomorphisms and Finite Gorenstein Dimension
• Homological aspects of semidualizing modules
• Foundations of relative homological algebra
• Stability of Gorenstein categories
• Stable module theory

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