On G-Regular Local Rings

DOI10.1080/00927870802179602zbMath1156.13009OpenAlexW2143179140MaRDI QIDQ5301513

Ryo Takahashi

Publication date: 20 January 2009

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

Full work available at URL: https://soar-ir.repo.nii.ac.jp/record/11921/files/On_G-Regular.pdf

zbMATH Keywords

matrix factorizationtotally reflexive moduleG-dimensionG-regular local ringKnörrer's periodicity

Mathematics Subject Classification ID

Homological dimension and commutative rings (13D05) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Cohen-Macaulay modules (13C14) Other special types of modules and ideals in commutative rings (13C13)

Related Items (29)

The almost Gorenstein Rees algebras over two-dimensional regular local rings ⋮ Totally reflexive modules and Poincaré series ⋮ Existence and Constructions of Totally Reflexive Modules ⋮ Testing for the Gorenstein property ⋮ Thick subcategories over isolated singularities ⋮ Ulrich ideals and 2-AGL rings ⋮ Reducing invariants and total reflexivity ⋮ Local rings with self-dual maximal ideal ⋮ The Auslander-Reiten conjecture for certain non-Gorenstein Cohen-Macaulay rings ⋮ Vanishing of Ext and Tor over fiber products ⋮ On the reducing projective dimension over local rings ⋮ Burch ideals and Burch rings ⋮ Totally reflexive modules over rings that are close to Gorenstein ⋮ On the vanishing of the theta invariant and a conjecture of Huneke and Wiegand ⋮ Almost Gorenstein rings - towards a theory of higher dimension ⋮ On the almost Gorenstein property of determinantal rings ⋮ Modules that detect finite homological dimensions ⋮ On the vanishing of self extensions over Cohen-Macaulay local rings ⋮ On the existence of non-free totally reflexive modules ⋮ The almost Gorenstein Rees algebras of parameters ⋮ Ulrich ideals and almost Gorenstein rings ⋮ Homological dimensions of rigid modules ⋮ Resolving subcategories whose finitely presented module categories are abelian ⋮ Brauer-Thrall for totally reflexive modules over local rings of higher dimension ⋮ Two generalizations of Auslander-Reiten duality and applications ⋮ Ulrich ideals in numerical semigroup rings of small multiplicity ⋮ On the new intersection theorem for totally reflexive modules ⋮ Unnamed Item ⋮ When is $R \ltimes I$ an almost Gorenstein local ring?

Cites Work

• Remarks on modules approximated by \(G\)-projective modules
• Finite Gorenstein representation type implies simple singularity
• Gorenstein dimensions
• Cohen-Macaulay modules on hypersurface singularities. I
• On the category of modules of Gorenstein dimension zero. II
• On the category of modules of Gorenstein dimension zero
• Bifurcation analysis of a vibropercussion system by the method of amplitude surface
• ABSOLUTE, RELATIVE, AND TATE COHOMOLOGY OF MODULES OF FINITE GORENSTEIN DIMENSION
• On the number of indecomposable totally reflexive modules
• An Uncountably Infinite Number of Indecomposable Totally Reflexive Modules

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