The Auslander-Bridger Formula And The Gorenstein Property For Coherent Rings

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. © 2009 Rocky Mountain Mathematics Consortium.