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 …

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 …

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 …

For any ring R we construct two triangulated categories, each admitting a functor from R-
modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

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 …

Let R be a ring (not necessarily commutative) and (ℒ, 𝒜) a bi-complete duality pair. We
investigate the notions of (flat-typed)(ℒ, 𝒜)-Gorenstein rings, which unify Iwanaga …

We introduce the notion of relative singularity category with respect to any self-orthogonal
subcategory $\omega $ of an abelian category. We introduce the Frobenius category of …

Let $\A $ be an abelian category, and $\V $, $\W $ two additive full subcategories of $\A $.
We introduce and study the $\V\W $-Gorenstein subcategory of $\A $, which unifies many …

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 …