Beyond totally reflexive modules and back: a survey on Gorenstein dimensions
LW Christensen, HB Foxby, H Holm - Commutative Algebra: Noetherian …, 2011 - Springer
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 …
homological dimensions for modules over commutative rings. The account includes the …
Reflexivity and rigidity for complexes, I: Commutative rings
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 …
noetherian ring R is introduced and studied. One of the main results characterizes C-rigid …
[PDF][PDF] Semidualizing modules
S Sather-Wagstaff - 2010 - ndsu.edu
Semidualizing modules have been found to be useful for several constructions in
homological algebra. Introduced by Foxby, Vasconcelos, Golod, and Wakamatsu. Studied …
homological algebra. Introduced by Foxby, Vasconcelos, Golod, and Wakamatsu. Studied …
Comparison of relative cohomology theories with respect to semidualizing modules
S Sather-Wagstaff, T Sharif, D White - Mathematische Zeitschrift, 2010 - Springer
We compare and contrast various relative cohomology theories that arise from resolutions
involving semidualizing modules. We prove a general balance result for relative …
involving semidualizing modules. We prove a general balance result for relative …
[HTML][HTML] Applications and homological properties of local rings with decomposable maximal ideals
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 …
satisfies the uniform Auslander condition (UAC), but the localization R p does not satisfy …
Semidualizing modules and the divisor class group
S Sather-Wagstaff - Illinois Journal of Mathematics, 2007 - projecteuclid.org
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 …
modules have been singled out due to their particularly nice duality properties. When $ R …
The set of semidualizing complexes is a nontrivial metric space
A Frankild, S Sather-Wagstaff - Journal of Algebra, 2007 - Elsevier
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 …
local ring R admits a nontrivial metric. We investigate the interplay between the metric and …
[HTML][HTML] Transfer of Gorenstein dimensions along ring homomorphisms
LW Christensen, S Sather-Wagstaff - Journal of Pure and Applied Algebra, 2010 - Elsevier
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 …
is to find resolution-free characterizations of the modules for which these invariants are finite …
Restricted injective dimensions over Cohen-Macaulay rings
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 …
Macaulay rings of finite Krull dimension. Based on this, and inspired by the recent work of …
[HTML][HTML] Complete intersection dimensions and Foxby classes
S Sather-Wagstaff - Journal of Pure and Applied Algebra, 2008 - Elsevier
Let R be a local ring and M a finitely generated R-module. The complete intersection
dimension of M–defined by Avramov, Gasharov and Peeva, and denoted–is a homological …
dimension of M–defined by Avramov, Gasharov and Peeva, and denoted–is a homological …