We prove that a finite dimensional algebra $ A $ with representation-finite subcategory
consisting of modules that are semi-Gorenstein-projective and $ n $-th syzygy modules is …

Gorenstein homological algebra is a kind of relative homological algebra which has been
developed to a high level since more than four decades. In this report we review the basic …

Let $ A $ be a virtually Gorenstein algebra of finite CM-type. We establish a duality between
the subcategory of compact objects in the homotopy category of Gorenstein projective left …

We first give precise connections between Auslander–Bridger's grade, double centraliser
properties and dominant dimension, and apply these to homological conjectures. Then we …

In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

We give new properties of algebras with finite Gorenstein dimension coinciding with the
dominant dimension $\geq 2$, which are called Auslander-Gorenstein algebras in the …

arXiv:math/9810152v2 [math.RA] 12 Feb 1999 Page 1 arXiv:math/9810152v2 [math.RA] 12
Feb 1999 GORENSTEINNESS OF INVARIANT SUBRINGS OF QUANTUM ALGEBRAS …

In basic homological algebra, the projective, injective and flat dimensions of modules play
an important and fundamental role. In this paper, the closely related Gorenstein projective …

One of the open problems in Gorenstein homological algebra is: when is the class of
Gorenstein injective modules closed under arbitrary direct limits? It is known that if the class …

We prove that algebras are left weakly Gorenstein in case the subcategory $^{\perp}
A\cap\Omega^ n (A) $ is representation-finite. This applies in particular to all monomial …