Lower and upper bounds for Cohen-Macaulay dimension

Abstract

Lower and upper bounds for CM-dimension, called CM*-dimension and CM*-dimension, will be defined for any finitely generated module M over a local Noetherian ring R. Both CM* and CM*-dimension reflect the Cohen-Macaulay property of rings. Our results will show that these dimensions have the expected basic properties parallel to those of the homological dimensions. In particular, they satisfy an analog of the Auslander-Buchsbaum formula. Copyright Clearance Centre, Inc.