COHEN-MACAULAY FLAT DIMENSION AND LOCAL HOMOLOGY MODULES

Let a be an ideal of a commutative Noetherian ring R, M a finitely generated R-module with finite flat dimension, and N an arbitrary R-module with finite Cohen-Macaulay flat dimension. We prove that the generalized local homology module H-i(a) (M,N) = 0 for each i larger than the Cohen-Macaulay flat dimension of N. As an application, we present a characterization for regularity of local rings having dualizing modules.