On Flat and Gorenstein Flat Dimensions of Local Cohomology Modules

摘要

Let a be an ideal of a Noetherian local ring R and let C be a semidualizing R-module. For an R-module X, we denote any of the quantities fd(R) X, Gfd(R) X and G(C)-fd(R) X by T(X). Let M be an R-module such that H-a(i) (M) = 0 for all i not equal n. It is proved that if T(M) < infinity, then T(H-a(n)(M)) <= T(M) + n, and the equality holds whenever M is finitely generated. With the aid of these results, among other things, we characterize Cohen-Macaulay modules, dualizing modules, and Gorenstein rings.