On a conjecture of Auslander and Reiten

DOI10.1016/j.jalgebra.2003.07.018zbMath1096.13011arXivmath/0305001OpenAlexW2008124099WikidataQ122897753 ScholiaQ122897753MaRDI QIDQ1883039

Craig Huneke, Graham J. Leuschke

Publication date: 1 October 2004

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

Full work available at URL: https://arxiv.org/abs/math/0305001

zbMATH Keywords

Cohen-Macaulay ringGorensteinlocally excellent ringprojectivity of module

Mathematics Subject Classification ID

Projective and free modules and ideals in commutative rings (13C10) Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07)

Related Items (32)

Homological aspects of derivation modules and critical case of the Herzog-Vasconcelos conjecture ⋮ The Auslander-Reiten Conjecture for Group Rings ⋮ On tensor products of rings and extension conjectures ⋮ Comparing complexities of pairs of modules ⋮ Necessary conditions for the depth formula over Cohen-Macaulay local rings ⋮ Generalized local duality, canonical modules, and prescribed bound on projective dimension ⋮ Maximal Cohen–Macaulay tensor products and vanishing of Ext modules ⋮ Auslander–Reiten conjecture of the tilting theorem ⋮ The Auslander-Reiten conjecture for certain non-Gorenstein Cohen-Macaulay rings ⋮ Vanishing of Ext and Tor over fiber products ⋮ Auslander-Reiten conjecture and finite injective dimension of \(\operatorname{Hom}\) ⋮ Gorenstein modifications and \mathds{𝑄}-Gorenstein rings ⋮ Auslander-Reiten conjecture and Auslander-Reiten duality ⋮ On the Auslander–Reiten conjecture for Cohen–Macaulay rings and path algebras ⋮ Tilting complexes and Auslander-Reiten conjecture. ⋮ Extremal growth of Betti numbers and trivial vanishing of (co)homology ⋮ On the vanishing of self extensions over algebras ⋮ Hom and Ext, revisited ⋮ Auslander-Reiten conjecture in a dual vein ⋮ When does the canonical module of a module have finite injective dimension? ⋮ Structure of irreducible homomorphisms to/from free modules ⋮ Algebras that satisfy Auslander's condition on vanishing of cohomology. ⋮ On the Auslander-Reiten conjecture for algebras ⋮ On the vanishing of self extensions over Cohen-Macaulay local rings ⋮ The Auslander-Reiten conjecture for Gorenstein rings ⋮ PROGRESS ON THE AUSLANDER–REITEN CONJECTURE ⋮ Two generalizations of Auslander-Reiten duality and applications ⋮ Criteria for prescribed bound on projective dimension ⋮ Generalized Auslander-Reiten Conjecture and Derived Equivalences ⋮ Extensions of a dualizing complex by its ring: Commutative versions of a conjecture of Tachikawa ⋮ On the Auslander–Reiten conjecture for Cohen–Macaulay local rings ⋮ Auslander-Reiten conjecture and special biserial algebras

Cites Work

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• Modules without self-extensions and Nakayama's conjecture
• A non-projective module without self-extensions
• Vanishing of Ext and Tor over some Cohen-Macaulay local rings
• Support varieties and cohomology over complete intersections
• Liftings and weak liftings of modules
• Some criteria for the Gorenstein property
• Divisor Class Groups and Deformations
• Pathologies IV
• On a Generalized Version of the Nakayama Conjecture
• GORENSTEIN MODULES, FINITE INDEX, AND FINITE COHEN–MACAULAY TYPE
• Stable module theory

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