Reflexivity and ring homomorphisms of finite flat dimension
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In this paper, the authors present a systematic study of the reflexivity properties of homologically finite complexes with respect to semidualizing complexes in the setting of nonlocal rings.Abstract:
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 primary focus is the descent of these properties over ring homomorphisms of finite flat dimension, presented in terms of inequalities between generalized G-dimensions. Most of these results are new even when the ring homomorphism is local. The main tool for these analyses is a nonlocal version of the amplitude inequality of Iversen, Foxby, and Iyengar. We provide numerous examples demonstrating the need for certain hypotheses and the strictness of many inequalities.read more
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Journal ArticleDOI
The set of semidualizing complexes is a nontrivial metric space
TL;DR: In this paper, it was shown that the set S (R ) of shift-isomorphism classes of semidualizing complexes over a local ring R admits a nontrivial metric.
Journal ArticleDOI
Reflexivity and rigidity for complexes, I: Commutative rings
TL;DR: In this article, a notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied, which leads to broad generalizations of theorems of Yekutieli and Zhang concerning rigid dualizing complexes, in the sense of Van den Bergh.
Journal ArticleDOI
Comparison of relative cohomology theories with respect to semidualizing modules
TL;DR: In this article, the authors compare and contrast relative cohomology theories that arise from resolutions involving semidualizing modules, and demonstrate the failure of the naive version of balance one might expect for these functors.
Book ChapterDOI
Beyond totally reflexive modules and back
TL;DR: In this paper, the authors survey the theory of Gorenstein homological dimensions for modules over commutative rings, including the connections with relative homological algebra and with studies of local ring homomorphisms.
Journal ArticleDOI
Semidualizing modules and the divisor class group
TL;DR: In this article, a natural inclusion of the set of isomorphism classes of semidualizing R-modules into the divisor class group of R over normal domains is presented.
References
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Book
Éléments de géométrie algébrique
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Book
Introduction to Commutative Algebra
TL;DR: It is shown here how the Noetherian Rings and Dedekind Domains can be transformed into rings and Modules of Fractions using the following structures:
Book
Commutative Ring Theory
Hideyuki Matsumura,Miles Reid +1 more
TL;DR: In this article, the authors introduce the notion of complete local rings and apply it to a wide range of applications, including: I-smoothness, I-flatness revisited, and valuation rings.
Book
Cohen-Macaulay rings
Winfried Bruns,H. Jürgen Herzog +1 more
TL;DR: In this article, the authors present a self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules.