The Auslander-Bridger formula and the Gorenstein property for coherent rings
Livia Hummel, Thomas Marley
TL;DR
This paper extends the Auslander-Bridger formula to coherent rings, developing a theory of Gorenstein rings in this broader context, and explores the Gorenstein property for finitely presented modules.
Contribution
It generalizes the Auslander-Bridger formula from Noetherian to coherent rings and advances the theory of coherent Gorenstein rings.
Findings
Generalized Auslander-Bridger formula for coherent rings
Established foundational properties of coherent Gorenstein rings
Connected Gorenstein dimension with module theory in coherent settings
Abstract
The concept of Gorenstein dimension, defined by Auslander and Bridger for finitely generated modules over a Noetherian ring, is studied in the context of finitely presented modules over a coherent ring. A generalization of the Auslander-Bridger formula is established and is used as a cornerstone in the development of a theory of coherent Gorenstein rings.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons