In the last two decades Cohen-Macaulay rings and modules have been central topics in
commutative algebra. This book meets the need for a thorough, self-contained introduction …

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 …

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

Let $ R $ be a commutative Noetherian ring. We study $ R $–modules, and complexes of
such, with excellent duality properties. While their common properties are strong enough to …

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 …

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

It is proved that for a commutative noetherian ring with dualizing complex the homotopy
category of projective modules is equivalent, as a triangulated category, to the homotopy …

We investigate the notion of the C-projective dimension of a module, where C is a
semidualizing module. When C= R, this recovers the standard projective dimension. We …

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is"
often" covering and preenveloping. As an application, we generalize a result by Enochs et …

We prove a version of Koszul duality and the induced derived equivalence for Adams
connected $ A_\infty $-algebras that generalizes the classical Beilinson-Ginzburg-Soergel …