Let R be a commutative Noetherian ring and A an Artinian R-module. We prove that if A has
finite Gorenstein injective dimension, then A possesses a Gorenstein injective envelope …

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

We consider a ring R such that the class of Gorenstein injective modules is closed under
direct limits. We prove that the class of dg-Gorenstein injective complexes is covering in Ch …

Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of
cohomology of finitely generated modules. The failure of this conjecture—by a 2003 …

Let $ R $ be a left coherent ring. It is proven that if an $ R $-module $ M $ has a finite FP-
injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and the …

Let $\varphi\colon R\rightarrow A $ be a ring homomorphism, where $ R $ is a commutative
noetherian ring and $ A $ is a finite $ R $-algebra. We give criteria for detecting the ascent …

Let S be a deeply embedded, equicharacteristic, Artinian Gorenstein local ring. We prove
that if R is a non-Gorenstein quotient of S of small colength, then every totally reflexive R …

Given a complete hereditary cotorsion pair-Gorenstein projective modules and study its
stability properties. As applications, we first get two model structures related to Gorenstein …

Let S and R be rings and _SC_R be a semidualizing bimodule. We first give the definitions
of C-transpose and nC-torsionfree and give a criterion for a module A to be G_C-projective …

For any ring R, we show that, in the bounded derived category Db (Mod R) of le R-modules,
the subcategory of complexes with nite Gorenstein projective (resp. injective) dimension …