Two generalizations of Auslander-Reiten duality and applications

TL;DR

This paper extends Auslander-Reiten duality in two ways and applies these results to establish new criteria for module freeness over local rings, contributing to the understanding of the Auslander-Reiten conjecture.

Contribution

It introduces two generalizations of Auslander-Reiten duality and applies them to derive criteria for module freeness based on Ext vanishing.

Findings

New criteria for module freeness over local rings

Recovery of known results on the Auslander-Reiten conjecture

Extensions of Auslander-Reiten duality

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.