Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative
noetherian ring R is introduced and studied. One of the main results characterizes C-rigid …

Semidualizing modules have been found to be useful for several constructions in
homological algebra. Introduced by Foxby, Vasconcelos, Golod, and Wakamatsu. Studied …

We compare and contrast various relative cohomology theories that arise from resolutions
involving semidualizing modules. We prove a general balance result for relative …

Among the finitely generated modules over a Noetherian ring $ R $, the semidualizing
modules have been singled out due to their particularly nice duality properties. When $ R …

We construct a local Cohen–Macaulay ring R with a prime ideal p∈ Spec (R) such that R
satisfies the uniform Auslander condition (UAC), but the localization R p does not satisfy …

We show that the set S (R) of shift-isomorphism classes of semidualizing complexes over a
local ring R admits a nontrivial metric. We investigate the interplay between the metric and …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

We show that the small and large restricted injective dimensions coincide for Cohen-
Macaulay rings of finite Krull dimension. Based on this, and inspired by the recent work of …

We answer a question of Celikbas, Dao, and Takahashi by establishing the following
characterization of Gorenstein rings: a commutative noetherian local ring (R,\mathfrak m)(R …