Let R be a commutative noetherian ring. Lindo and Pande have recently posed the question
asking when every ideal of R is isomorphic to some trace ideal of R. This paper studies this …

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 …

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 prove two theorems on the vanishing of Ext over commutative Noetherian local rings.
Our first theorem shows that, over non-regular Cohen-Macaulay local domains, there are no …

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 …

In this article we present a systematic study of the reflexivity properties of homologically finite
complexes with respect to semidualizing complexes in the setting of nonlocal rings. One …

Let R be a Cohen–Macaulay local ring and let M and N be finitely generated R-modules. In
this paper we investigate some of the necessary conditions for the depth formula depth (M)+ …

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 …

A degree of a module $ M $ is a numerical measure of information carried by $ M $. We
highlight some of Vasconcelos' outstanding contributions to the theory of degrees, bridging …