The flat stable module category of a coherent ring

TL;DR

This paper constructs a new abelian model structure on the category of modules over a right coherent ring, characterizing Gorenstein flat modules as cofibrant objects and establishing a key equivalence involving flat and cotorsion modules.

Contribution

It introduces a novel method for building model structures and characterizes flat and cotorsion modules via Gorenstein conditions.

Findings

Established an abelian model structure with Gorenstein flat modules as cofibrants

Proved the equivalence between flat and cotorsion modules and Gorenstein flat and cotorsion modules

Provided a new approach for constructing model structures in module categories

Abstract

Let $R$ by a right coherent ring and $R$-Mod denote the category of left $R$-modules. We show that there is an abelian model structure on $R$-Mod whose cofibrant objects are precisely the Gorenstein flat modules. Employing a new method for constructing model structures, the key step is to show that a module is flat and cotorsion if and only if it is Gorenstein flat and Gorenstein cotorsion.