In a paper from 2002, Hovey introduced the Gorenstein projective and Gorenstein injective
model structures on R-Mod, the category of R-modules, where R is any Gorenstein ring …

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 …

Let R be any ring with identity and Ch (R) C h (R) the category of chain complexes of (left) R-
modules. We show that the Gorenstein AC-projective chain complexes of 1 are the cofibrant …

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides
a starting point to study the relationship between homological and homotopical algebra, a …

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 …

We introduce what is meant by an AC-Gorenstein ring. It is a generalized notion of
Gorenstein ring that is compatible with the Gorenstein AC-injective and Gorenstein AC …

A model structure on a category is a formal way of introducing a homotopy theory on that
category, and if the model structure is abelian and hereditary, its homotopy category is …

We study Gorenstein flat objects in the category Rep (Q, R) of representations of a left rooted
quiver Q with values in Mod (R), the category of all left R-modules, where R is an arbitrary …

We study homotopy categories of model categories arising from a cotorsion triple, and the
equivalences between corresponding stable categories. We characterize homological …

Absolutely clean and level R-modules were introduced in and used to show how Gorenstein
homological algebra can be extended to an arbitrary ring R. This led to the notion of …