On Gorenstein projective, injective and flat dimensions -- a functorial description with applications

From MaRDI portal
Publication:852674

DOI10.1016/j.jalgebra.2005.12.007zbMath1104.13008arXivmath/0403156OpenAlexW2100487368WikidataQ123365250 ScholiaQ123365250MaRDI QIDQ852674

Lars Winther Christensen, Henrik Holm, Anders J. Frankild

Publication date: 15 November 2006

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

Full work available at URL: https://arxiv.org/abs/math/0403156


zbMATH Keywords

Bass formulaAuslander categoriesChouinard formulaFoxby equivalence


Mathematics Subject Classification ID

Homological dimension and commutative rings (13D05) Homological dimension in associative algebras (16E10)


Related Items

Semi-dualizing modules and related Gorenstein homological dimensions ⋮ Pseudo-dualizing complexes of bicomodules and pairs of t-structures ⋮ Tests for injectivity of modules over commutative rings ⋮ New characterizations of restricted injective dimensions for complexes ⋮ Applications of balanced pairs ⋮ A relative silting theorem ⋮ Modules of finite homological dimension with respect to a semidualizing module ⋮ A generalization of Gorenstein injective modules ⋮ Transfer of Gorenstein dimensions along ring homomorphisms ⋮ Cotorsion pairs induced by duality pairs ⋮ Tate homology of modules of finite Gorenstein flat dimension. ⋮ Zaks' lemma for coherent rings. ⋮ Vanishing of Tate homology -- an application of stable homology for complexes ⋮ Gorenstein dimension of modules over homomorphisms ⋮ Complete cohomology for complexes with finite Gorenstein AC-projective dimension ⋮ Totally acyclic complexes ⋮ Virtually Gorenstein rings and relative homology of complexes ⋮ The depth formula for modules with reducible complexity ⋮ Cotorsion pairs associated with Auslander categories ⋮ Gorenstein homological dimensions and Auslander categories ⋮ Separated monic representations. I: Gorenstein-projective modules ⋮ Cosupport computations for finitely generated modules over commutative noetherian rings ⋮ On Gorenstein flat preenvelopes of complexes. ⋮ Level and Gorenstein projective dimension ⋮ Finiteness conditions and relative derived categories ⋮ Resolving resolution dimensions ⋮ Dedualizing complexes of bicomodules and MGM duality over coalgebras ⋮ Modules with cosupport and injective functors. ⋮ Pure-minimal chain complexes ⋮ Relative derived categories ⋮ Strongly Gorenstein projective, injective, and flat modules ⋮ Gorenstein derived equivalences and their invariants ⋮ The Bongartz's theorem on the homotopy category ⋮ Ding projective modules with respect to a semidualizing bimodule. ⋮ When the kernel of a complete hereditary cotorsion pair is the additive closure of a tilting module ⋮ Stable \(t\)-structures and homotopy category of Gorenstein-projective modules ⋮ Homotopy equivalences induced by balanced pairs ⋮ On the Gorenstein defect categories ⋮ A unified approach to formal local cohomology and local Tate cohomology ⋮ Change of rings and singularity categories ⋮ Torsionfree dimension of modules and self-injective dimension of rings. ⋮ Preservation of quasi-isomorphisms of complexes ⋮ Remarks on balance for Tate and generalized Tate (co)homology ⋮ Gorenstein syzygy modules. ⋮ Brauer-Thrall for totally reflexive modules ⋮ Gorenstein dimensions of unbounded complexes and change of base (with an appendix by Driss Bennis) ⋮ Gorensteinness, homological invariants and Gorenstein derived categories ⋮ Quillen equivalences for stable categories ⋮ Linkage of modules with respect to a semidualizing module ⋮ A model structure approach to the Tate-Vogel cohomology ⋮ Relative cohomology of complexes II: vanishing of relative cohomology ⋮ Vanishing of stable homology with respect to a semidualizing module ⋮ Categorical resolutions of a class of derived categories ⋮ Relative cohomology of complexes ⋮ The right Gorenstein subcategory \(r\mathcal{G}(\mathscr{C},\mathscr{D})\) ⋮ Proper resolutions and Gorenstein categories ⋮ Hopf extensions of CM-finite Artin algebras ⋮ Gorenstein global dimension of an amalgamated duplication of a coherent ring along an ideal ⋮ A refinement of Gorenstein flat dimension via the flat-cotorsion theory ⋮ Relative singularity categories. II ⋮ Vanishing of Tate homology and depth formulas over local rings ⋮ Gorenstein projective dimensions of complexes. ⋮ Three results on Frobenius categories ⋮ Tate cohomology for complexes with finite Gorenstein AC-injective dimension ⋮ Adic Foxby classes ⋮ Subprojectivity in abelian categories ⋮ Gorenstein injective filtrations over Cohen-Macaulay rings with dualizing modules ⋮ Duality pairs induced by Gorenstein projective modules with respect to semidualizing modules ⋮ Complete intersection dimensions and Foxby classes ⋮ Vanishing of relative homology and depth of tensor products ⋮ Gorenstein homology, relative pure homology and virtually Gorenstein rings ⋮ Coherent rings, fp-injective modules, dualizing complexes, and covariant Serre-Grothendieck duality ⋮ Strongly Gorenstein projective, injective and flat modules. ⋮ Gorenstein projective precovers ⋮ On Gorenstein projective dimensions of unbounded complexes ⋮ A construction of Gorenstein-projective modules. ⋮ A smashing subcategory of the homotopy category of Gorenstein projective modules ⋮ Gorenstein derived categories ⋮ Algebras that satisfy Auslander's condition on vanishing of cohomology. ⋮ Gorenstein singularity categories ⋮ On (strongly) Gorenstein (semi)hereditary rings ⋮ (Weak) Gorenstein global dimension of semiartinian rings ⋮ Characterizing local rings via homological dimensions and regular sequences ⋮ DC-projective dimensions, Foxby equivalence and SDC-projective modules ⋮ The homological theory of quasi-resolving subcategories ⋮ Strongly Gorenstein flat modules and dimensions. ⋮ Strongly Gorenstein Flat Dimensions of Complexes ⋮ Complete intersection Hom injective dimension ⋮ Gorenstein injective complexes of modules over Noetherian rings. ⋮ Resolving resolution dimensions in triangulated categories ⋮ On Balance for Relative Homology ⋮ Homology theories and Gorenstein dimensions for complexes ⋮ Gorenstein Modules and Auslander Categories ⋮ Some criteria for the Cohen-Macaulay property and local cohomology ⋮ Pseudo-dualizing complexes and pseudo-derived categories ⋮ A Bass equality for Gorenstein injective dimension of modules finite over homomorphisms ⋮ Balance for relative (co)homology in abelian categories ⋮ Finiteness criteria in quasi-resolving subcategories ⋮ Relative singularity categories ⋮ On pure derived categories ⋮ Homological dimension based on a class of Gorenstein flat modules ⋮ Finiteness criteria for Gorenstein flat dimension and stability ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Dimension of complexes related to special Gorenstein projective precovers(II) ⋮ LOCAL HOMOLOGY AND GORENSTEIN FLAT MODULES ⋮ COHERENT RINGS AND GORENSTEIN YOKE MODULES ⋮ Gorenstein projective and flat complexes over noetherian rings ⋮ Notes on linkage of modules with respect to a semidualizing module ⋮ Complexes of FP-injective Modules ⋮ Gorenstein Modules and Dualizing Modules ⋮ Quasi-Gorenstein projective and quasi-Gorenstein injective modules ⋮ G-Gorenstein Modules ⋮ Contracting endomorphisms and dualizing complexes ⋮ Unnamed Item ⋮ Finiteness criteria in Gorenstein homological algebra ⋮ Endomorphism algebras of Gorenstein projective modules ⋮ GORENSTEIN DIMENSIONS MODULO A REGULAR ELEMENT ⋮ Cohen factorizations and Gorenstein dimensions ⋮ Detecting completeness from Ext-vanishing ⋮ Gorenstein FC-projective modules ⋮ Unnamed Item ⋮ Gorenstein projective modules and recollements over triangular matrix rings ⋮ Stable homology over associative rings ⋮ GORENSTEIN MODULES AND GORENSTEIN MODEL STRUCTURES ⋮ Gorenstein homological dimensions and some duality results ⋮ Stable local cohomology ⋮ On the Gorenstein dimensions over local homomorphisms ⋮ Recollements of Gorenstein derived categories ⋮ SG_C-Projective, Injective and Flat modules ⋮ One-sided Gorenstein subcategories ⋮ $VW$-Gorenstein complexes ⋮ EMBEDDING MODULES OF FINITE HOMOLOGICAL DIMENSION ⋮ The orthogonal complement relative to the functor extension of the class of all Gorenstein flat modules ⋮ Auslander–Reiten Triangles on Gorenstein Derived Categories ⋮ Tate homology with respect to cotorsion pairs ⋮ Tate (co)homology via pinched complexes ⋮ Gorenstein Projective Dimension Relative to a Semidualizing Bimodule ⋮ Vanishing of Tate Cohomology and Gorenstein Injective Dimension ⋮ Gorenstein Homological Dimensions of Complexes with Respect to a Semidualizing Module ⋮ On the Existence of Certain Modules of Finite Gorenstein Homological Dimensions ⋮ A QUILLEN MODEL STRUCTURE APPROACH TO HOMOLOGICAL DIMENSIONS OF COMPLEXES ⋮ On Restricted Injective Dimensions of Complexes ⋮ Gorenstein Right Derived Functors of − ⊗ −with Respect to Semidualizing Modules ⋮ Transfer of Gorenstein Dimensions of Unbounded Complexes Along Ring Homomorphisms ⋮ On F-Gorenstein dimensions ⋮ Relative stable (co)homology ⋮ DERIVED CATEGORIES WITH RESPECT TO DING MODULES ⋮ A note on Gorenstein projective modules ⋮ A test complex for Gorensteinness ⋮ A Bass Formula for Gorenstein Injective Dimension ⋮ Gorenstein injectivity of the section functor ⋮ First, Second, and Third Change of Rings Theorems for Gorenstein Homological dimensions ⋮ Gorenstein Injective Resolutions, Cousin Complexes and Top Local Cohomology Modules ⋮ Cohen-Macaulay homological dimensions ⋮ A Note on Gorenstein Flat Dimension ⋮ PERIODIC SHORT EXACT SEQUENCES AND PERIODIC PURE-EXACT SEQUENCES ⋮ Some results on $G_C$-flat dimension of modules ⋮ Two filtration results for modules with applications to the Auslander condition ⋮ C-Gorenstein projective, injective and flat modules ⋮ Unnamed Item ⋮ Symmetric Auslander and Bass categories ⋮ Wide subcategories of 𝑑-cluster tilting subcategories ⋮ RIGHT GORENSTEIN GLOBAL DIMENSION OF AN (ALMOST) EXCELLENT EXTENSION ⋮ Finiteness of Gorenstein injective dimension of modules ⋮ On triangle equivalences of stable categories ⋮ Gorenstein Projective, Injective, and Flat Complexes ⋮ A GENERALIZATION OF STRONGLY GORENSTEIN PROJECTIVE MODULES ⋮ Cohen-Macaulay homological dimensions ⋮ Gorenstein Global Dimensions and Cotorsion Dimension of Rings ⋮ Gorenstein AC-projective dimension of unbounded complexes ⋮ Gorenstein homological properties for Hopf--Galois extensions ⋮ STRONGLY GORENSTEIN FLAT MODULES ⋮ n-Strongly Gorenstein Projective, Injective and Flat Modules ⋮ On (Strongly) Gorenstein Von Neumann Regular Rings ⋮ Matrix factorizations for self-orthogonal categories of modules ⋮ Gorenstein Injective Dimension for Complexes and Iwanaga–Gorenstein Rings ⋮ A construction of relative left derived functors similar to $\operatorname {Tor}$ ⋮ Gorenstein Injective Envelopes of Artinian Modules ⋮ Gorenstein injective covers and envelopes over noetherian rings ⋮ Gorenstein Flat and Cotorsion Dimensions of Unbounded Complexes ⋮ A Gorenstein analogue of a result of Bertin ⋮ Gorenstein Analogue of Auslander's Theorem on the Global Dimension ⋮ STABILITY OF GORENSTEIN FLAT MODULES ⋮ STABILITY OF GORENSTEIN FLAT CATEGORIES ⋮ GorensteinFP-Injective Dimension for Complexes ⋮ Finiteness of Selfinjective Dimension for Noetherian Algebras ⋮ The existence of finitely generated modules of finite Gorenstein injective dimension ⋮ GORENSTEIN PROJECTIVE, INJECTIVE AND FLAT MODULES ⋮ On Gorenstein flat dimension ⋮ Cotorsion Dimension of Unbounded Complexes ⋮ Gorenstein Dimensions over Ring Homomorphisms ⋮ Stability of Gorenstein Classes of Modules ⋮ Totally acyclic complexes and locally Gorenstein rings ⋮ Totally reflexive modules with respect to a semidualizing bimodule ⋮ Notes on resolving resolution dimensions ⋮ BALANCE FOR TATE COHOMOLOGY WITH RESPECT TO SEMIDUALIZING MODULES ⋮ COHEN-MACAULAY HOMOLOGICAL DIMENSIONS WITH RESPECT TO AMALGAMATED DUPLICATION ⋮ Dimension of complexes related to special Gorenstein projective precovers ⋮ FP-injective dimensions and Gorenstein homology ⋮ Relative and Tate homology with respect to semidualizing modules ⋮ On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence ⋮ Gorenstein injective envelopes and covers over two sided noetherian rings



Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:852674&oldid=12796418"
Powered by MediaWiki