Totally reflexive extensions and modules

TL;DR

This paper introduces totally reflexive extensions of rings, unifying Gorenstein orders and Frobenius extensions, and characterizes totally reflexive modules over these extensions in terms of modules over the base ring.

Contribution

It defines the concept of totally reflexive extensions and establishes a key equivalence for modules over these extensions and base rings.

Findings

Unifies Gorenstein orders and Frobenius extensions under a new framework

Provides a characterization of totally reflexive modules over extensions

Establishes an equivalence between modules over the extension and base ring

Abstract

We introduce the notion of totally reflexive extension of rings. It unifies Gorenstein orders and Frobenius extensions. We prove that for a totally reflexive extension, a module over the extension ring is totally reflexive if and only if its underlying module over the base ring is totally reflexive.