Auslander--Reiten conjecture for normal rings

TL;DR

This paper proves the Auslander--Reiten conjecture for all normal rings by establishing conditions under which finitely generated modules are projective based on Ext module vanishing.

Contribution

It provides a proof of the Auslander--Reiten conjecture for normal rings, expanding the class of rings where the conjecture is confirmed.

Findings

Auslander--Reiten conjecture holds for all normal rings

Provides conditions for projectivity of modules via Ext vanishing

Advances understanding of module theory over normal rings

Abstract

In this paper, sufficient conditions for finitely generated modules over a commutative noetherian ring to be projective are given in terms of vanishing of Ext modules. One of the main results of this paper asserts that the Auslander--Reiten conjecture holds true for every normal ring.