Some applications of Cohen-Macaulay injective dimension

Abstract

Let a be an ideal of a commutative Noetherian ring R, M a finitely generated R-module with finite projective dimension and N an arbitrary R-module with finite Cohen-Macaulay injective dimension. In this paper, we show that the generalized local cohomology Hi a(M, N) is zero for every i larger than the Cohen-Macaulay injective dimension of N. As applications, we obtain new characterizations of Gorenstein and regular local rings.