We obtain the Gorenstein flat model structure on the category Mod (R) of left R-modules
provided R is a GF-closed ring. Our approach does not rely on the coherence of the ring and
so it is necessarily different from the same Gorenstein flat model structure obtained by
Gillespie for coherent rings. Our technique can be extended to get new models for
Gorenstein flat modules relative to other contexts, like the so-called Gorenstein AC-flat
modules. 1. Introduction and preliminaries. In a recent paper [Gil17, Theorem 3.3], James …

A recent result by J. Šaroch and J. Šťovíček asserts that there is a unique abelian model
structure on the category of left R-modules, for any associative ring R with identity, whose
(trivially) cofibrant and (trivially) fibrant objects are given by the classes of Gorenstein flat
(resp., flat) and cotorsion (resp., Gorenstein cotorsion) modules. In this paper, we generalise
this result to a certain relativisation of Gorenstein flat modules, which we call Gorenstein B-
flat modules, where B is a class of right R-modules. Using some of the techniques …