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 f(I)(R) and the equidimensionalness of certain homomorphic images of R. As a consequence we deduce that f(I)(R) = max{1, ht I}, and if mAss(R) (R/I) is contained in AssR (R), then the ring R/I + U-n >= 1(0 :(R) I-n) is equidimensional of dimension dim R-1. Moreover, we will obtain a lower bound for injective dimension of the local cohomology module H-I(ht) (I)(R), in the case where (R, m) is a complete equidimensional local ring.