Gorenstein Projective Dimension Relative to a Semidualizing Bimodule

DOI10.1080/00927872.2011.602782zbMath1287.16015OpenAlexW2043301408MaRDI QIDQ4912713

Zeng Feng Liu, Aimin Xu, Zhao Yong Huang

Publication date: 5 April 2013

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

Full work available at URL: https://doi.org/10.1080/00927872.2011.602782

zbMATH Keywords

projective modulesAuslander classesGorenstein projective dimensionsemidualizing bimodulesFoxby equivalenceBass classes

Mathematics Subject Classification ID

Syzygies, resolutions, complexes in associative algebras (16E05) Homological dimension (category-theoretic aspects) (18G20) Relative homological algebra, projective classes (category-theoretic aspects) (18G25) Homological dimension in associative algebras (16E10)

Related Items

Homological dimensions relative to preresolving subcategories. II ⋮ G_C-projectivity and injectivity under Frobenius extensions ⋮ FP_n-injective and FP_n-flat modules with respect to a semidualizing bimodule ⋮ Relative Gorenstein flat modules and dimension ⋮ Foxby equivalences associated to Gorenstein categories𝒢(𝒳,𝒴,𝒵) ⋮ The role of w-tilting modules in relative Gorenstein (co)homology ⋮ Ding projective modules with respect to a semidualizing bimodule. ⋮ A unified approach to various Gorenstein modules ⋮ Cohen-Macaulay Noetherian algebras ⋮ On the \(C\)-flatness and injectivity of character modules ⋮ Proper resolutions and Gorenstein categories ⋮ Syzygy and torsionless modules with respect to a semidualizing module ⋮ One-sided Gorenstein subcategories ⋮ $\V\W$-Gorenstein categories ⋮ $VW$-Gorenstein complexes ⋮ Relative copure modules and Foxby equivalence ⋮ Coreflexive modules and semidualizing modules with finite projective dimension ⋮ Homological invariants related to semidualizing bimodules ⋮ Unnamed Item ⋮ Relative Gorenstein dimensions ⋮ Unnamed Item ⋮ On Balance for Relative Homology ⋮ Duality pairs induced by one-sided Gorenstein subcategories ⋮ Duality pairs induced by Auslander and Bass classes ⋮ Lamron ℓ-groups ⋮ Left orthogonal classes of semidualizing bimodules ⋮ On relative counterpart of Auslander’s conditions

Cites Work

• Gorenstein projective dimension with respect to a semidualizing module
• Tate cohomology with respect to semidualizing modules
• \(\mathcal W\)-Gorenstein modules
• Semi-dualizing modules and related Gorenstein homological dimensions
• On Gorenstein projective, injective and flat dimensions -- a functorial description with applications
• Gorenstein dimension of modules over homomorphisms
• Injective and flat covers, envelopes and resolvents
• Gorenstein homological dimensions.
• Gorenstein injective and projective modules
• ABSOLUTE, RELATIVE, AND TATE COHOMOLOGY OF MODULES OF FINITE GORENSTEIN DIMENSION
• Homological aspects of semidualizing modules
• Stability of Gorenstein categories
• Stable module theory