We apply ideas from commutative algebra, and Morita theory to algebraic topology using
ring spectra. This allows us to prove new duality results in algebra and topology, and to view …

The paper explores dualizing differential graded (DG) modules over DG algebras. The focus
is on DG algebras that are commutative local, and finite. One of the main results established …

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 …

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 …

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 …

Given an associative ring $ A $, we present a new approach for establishing the finiteness of
the big finitistic projective dimension $\operatorname {FPD}(A) $. The idea is to find a …

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 …

In this paper we study a connective commutative differential graded algebra (CDGA) which
is piecewise Noetherian. The principal aim is to analyze a dualizing complex of CDGA's and …