In the recent paper" The Nakayama functor and its completion for Gorenstein algebras", a
class of Gorenstein algebras over commutative noetherian rings was introduced, and duality …

Duality properties are studied for a Gorenstein algebra that is finite and projective over its
center. Using the homotopy category of injective modules, it is proved that there is a local …

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 …

We introduce a notion of Gorenstein R-algebras over a commutative Gorenstein ring R.
Then we provide a necessary and sufficient condition for a tilting complex over a Gorenstein …

In this paper we construct Gorenstein-projective modules over Morita rings with zero
bimodule homomorphisms and we provide sufficient conditions for such rings to be …

We generalise notions of Gorenstein homological algebra for rings to the context of arbitrary
abelian categories. The results are strongest for module categories of rngs with enough …

The monomorphism category S n (X) is introduced, where X is a full subcategory of the
module category A-mod of an Artin algebra A. The key result is a reciprocity of the …

Gorenstein homological algebra is an important area of mathematics, with applications in
commutative and noncommutative algebra, model category theory, representation theory …

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

Let A be a finite-dimensional Gorenstein algebra of finite CM-type. We show that the
Gorenstein derived category of A has Auslander–Reiten triangles. In this case, we otain a …