Gorenstein homological theory for differential modules

TL;DR

This paper establishes a fundamental equivalence between Gorenstein projective and injective properties of differential modules and their underlying modules, simplifying the understanding of Gorenstein homological properties in differential modules.

Contribution

It proves that Gorenstein projective and injective properties of differential modules are equivalent to those of their underlying modules, providing a key link in Gorenstein homological theory.

Findings

Differential module is Gorenstein projective iff its underlying module is Gorenstein projective.

Differential module is Gorenstein injective iff its underlying module is Gorenstein injective.

Establishes a duality between Gorenstein projective and injective differential modules.

Abstract

We show that a differential module is Gorenstein projective if and only if its underlying module is Gorenstein projective. Dually, a differential module is Gorenstein injective if and only if its underlying module is Gorenstein injective.