When are n-syzygy modules n-torsionfree?

TL;DR

This paper investigates the conditions under which n-syzygy modules over a commutative noetherian ring are n-torsionfree, using Serre's condition and local Gorenstein properties, extending Evans and Griffith's theorem.

Contribution

It provides new criteria linking n-syzygy modules and n-torsionfree modules, including the converse of a well-known theorem.

Findings

Established conditions under which n-syzygy modules are n-torsionfree.

Extended Evans and Griffith's theorem to the converse direction.

Utilized Serre's condition and local Gorenstein properties in the analysis.

Abstract

Let R be a commutative noetherian ring. We consider the question of when n-syzygy modules over R are n-torsionfree in the sense of Auslander and Bridger. Our tools include Serre's condition and certain conditions on the local Gorenstein property of R. Our main result implies the converse of a celebrated theorem of Evans and Griffith.