Gorenstein homological dimensions are refinements of the classical homological
dimensions, and finiteness singles out modules with amenable properties reflecting those of …

We extend the definition of a semidualizing module to general associative rings. This
enables us to define and study Auslander and Bass classes with respect to a semidualizing …

Let X be a chain complex over a commutative noetherian ring R, that is, an object in the
derived category 𝒟 (R). We investigate the small support and co-support of X, introduced by …

Let A be an associative non-positive differential graded ring. In this paper we make a
detailed study of a category Inj (A) of left DG-modules over A which generalizes the category …

We consider commutative DG rings (better known as nonpositive strongly commutative
associative unital DG algebras). For such a DG ring $ A $ we define the notions of perfect …

By extending some basic results of Grothendieck and Foxby about local cohomology to
commutative DG-rings, we prove new amplitude inequalities about finite DG-modules of …

We study the small and big finitistic projective, injective and flat dimensions over a non-
positively graded commutative noetherian DG-ring $ A $ with bounded cohomology. Our …

In this paper we present a new approach to Grothendieck duality over commutative rings.
Our approach is based on the idea of rigid dualizing complexes, which was introduced by …

When the base connected cochain DG algebra is cohomologically bounded, it is proved that
the difference between the amplitude of a compact DG module and that of the DG algebra is …

Abstract We prove a Cohen-Macaulay version of a result by Avramov-Golod and Frankild-
Jørgensen about Gorenstein rings, showing that if a noetherian ring A is Cohen-Macaulay …