Faltings’ Finiteness Dimension of Local Cohomology Modules Over Local Cohen–Macaulay Rings

Let (R, m) denote a local Cohen–Macaulay ring and I a non-nilpotent ideal of R. The purpose of this article is to investigate Faltings’ finiteness dimension fI(R) and the equidimensionalness of certain homomorphic images of R. As a consequence we deduce that fI(R) = max{1, ht I}, and if mAssR(R/I) is contained in AssR(R), then the ring is equidimensional of dimension dim R−1. Moreover, we will obtain a lower bound for injective dimension of the local cohomology module , in the case where (R,m) is a complete equidimensional local ring.