The existence of the Gorenstein projective precovers over arbitrary rings is an open
question. It is known that if the ring has finite Gorenstein global dimension, then every …

It is a well-known result of Auslander and Reiten that contravariant finiteness of the class P∞
fin (of finitely generated modules of finite projective dimension) over an Artin algebra is a …

Let (C, E, s) be an extriangulated category with a proper class ξ of E-triangles. We study
complete cohomology of objects in (C, E, s) by applying ξ-projective resolutions and ξ …

We study homological behavior of modules satisfying the Auslander condition. Assume that
AC is the class of left R-modules satisfying the Auslander condition. It is proved that each …

We construct a non-affine analogue of the singularity category of a Gorenstein local ring.
With this, Buchweitz's classic equivalence of three triangulated categories over a Gorenstein …