The relation between the Auslander (resp., Bass) class and the class of modules with finite
Gorenstein projective (resp., injective) dimension is well known when these mentioned …

Since Eilenberg and Moore [EM], the relative homological algebra, especially the
Gorenstein homological algebra ([EJ2]), has been developed to an advanced level. The …

Let A and B be rings, U a (B, A)-bimodule, and T= A 0 UB the triangular matrix ring. In this
paper, several notions in relative Gorenstein algebra over a triangular matrix ring are …

We study singularity categories through Gorenstein objects in triangulated categories and
silting theory. Let ω be a presilting subcategory of a triangulated category T. We introduce …

Work of J. Rickard proves that the derived module categories of two ringsAandBare
equivalent as triangulated categories if and only if there is a particular objectT, a so-called …

We study approximations of modules of finite Gorenstein flat dimension by (projectively
coresolved) Gorenstein flat modules and modules of finite flat dimension. These …

We introduce the concepts of generalized compatible and cocompatible bimodules in order
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …

In this article, we give a new characterization of Gorenstein projective modules. As
applications of our result, we prove that a strongly Gorenstein projective module of …

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 …

In this paper, we apply intermediate extension functors associated to certain recollements of
functor categories to study relative Auslander algebras. In particular, we study the existence …