Existence of Totally Reflexive Modules via Gorenstein Homomorphisms

TL;DR

This paper introduces a new class of local rings with non-trivial totally reflexive modules using Gorenstein homomorphisms, and provides a general construction demonstrating their abundance.

Contribution

It defines a class of local rings via Gorenstein homomorphisms that admit non-trivial totally reflexive modules and offers a construction method showing these rings are plentiful.

Findings

Existence of non-trivial totally reflexive modules over certain local rings

Construction method for such rings demonstrating their abundance

Framework linking Gorenstein homomorphisms to reflexive modules

Abstract

We define, via Gorenstein homomorphisms, a class of local rings over which there exist non-trivial totally reflexive modules. We also provide a general construction of such rings, which indicates their abundance.