Two generalizations of Auslander-Reiten duality and applications
arXiv:1807.00380 · doi:10.1215/00192082-7768744
Abstract
This paper extends Auslander-Reiten duality in two directions. As an application, we obtain various criteria for freeness of modules over local rings in terms of vanishing of Ext modules, which recover a lot of known results on the Auslander-Reiten conjecture.