On the Auslander–Reiten conjecture for Cohen–Macaulay local rings

DOI10.1090/proc/13487zbMath1374.13022OpenAlexW2532669828WikidataQ123225221 ScholiaQ123225221MaRDI QIDQ5270131

Shiro Goto, Ryo Takahashi

Publication date: 22 June 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13487

zbMATH Keywords

Cohen-Macaulay ringGorenstein ringsemidualizing moduleAuslander-Reiten conjectureTachikawa conjecture

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Homological conjectures (intersection theorems) in commutative ring theory (13D22)

Related Items (13)

Trace ideals of semidualizing modules and two generalizations of nearly Gorenstein rings ⋮ Generalized local duality, canonical modules, and prescribed bound on projective dimension ⋮ On the ideal case of a conjecture of Auslander and Reiten ⋮ Auslander-Reiten conjecture and finite injective dimension of \(\operatorname{Hom}\) ⋮ On the vanishing of self extensions over algebras ⋮ Hom and Ext, revisited ⋮ When does the canonical module of a module have finite injective dimension? ⋮ On the vanishing of self extensions over Cohen-Macaulay local rings ⋮ On the Ideal Case of a Conjecture of Huneke and Wiegand ⋮ Residually faithful modules and the Cohen-Macaulay type of idealizations ⋮ Two generalizations of Auslander-Reiten duality and applications ⋮ Criteria for prescribed bound on projective dimension ⋮ On the freeness of dual semidualizing modules

Cites Work

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• Huneke-Wiegand conjecture and change of rings
• Algebras that satisfy Auslander's condition on vanishing of cohomology.
• On a conjecture of Auslander and Reiten
• Some criteria for the Gorenstein property
• Extensions of a dualizing complex by its ring: Commutative versions of a conjecture of Tachikawa
• Semi-dualizing complexes and their Auslander categories
• Gorenstein Modules and Related Modules.
• The Auslander-Reiten conjecture for Gorenstein rings
• On the structure of closed ideals

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