On a conjecture of Auslander and Reiten

2003/04/30 by Craig Huneke, Huneke, Craig, Graham Leuschke +1
Mathematics · #13D07 #16E30 #16G50 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.RA #msc:13D07 #msc:16E30 #msc:16G50

paper · pdf · doi:10.48550/arxiv.math/0305001

12 pages, minor changes, this version to appear

arxiv created 2003/07/16 · arxiv updated 2009/11/30

Abstract

In studying Nakayama's 1958 conjecture on rings of infinite dominant dimension, Auslander and Reiten proposed the following generalization: Let Lambda be an Artin algebra and M a Lambda-generator such that Extⁱ_Lambda(M,M)=0 for all i ≥ 1; then M is projective. This conjecture makes sense for any ring. We establish Auslander and Reiten's conjecture for excellent Cohen--Macaulay normal domains containing the rational numbers, and slightly more generally.

Related

• Auslander--Reiten conjecture for normal rings
• On the ideal case of a conjecture of Auslander and Reiten
• Auslander-Reiten annihilators
• The Auslander-Reiten conjecture for certain non-Gorenstein Cohen-Macaulay rings
• Singular equivalences and Auslander-Reiten conjecture