On Flat and Gorenstein Flat Dimensions of Local Cohomology Modules

Abstract

AbstractLet 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 fdR X, GfdR X and GC-fdR X by T(X). Let M be an R-module such that for all i ≠ n. It is proved that if T(M) < ∞, then , 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.