Let R be a commutative Noetherian ring, an ideal of R, and M an R-module. We prove that for a fixed non-negative integer n, the nth local cohomology module Hn M is finitely generated if and only if Hn M is -cofinite and ⊆ 0 R Hn M. This enables us to establish the Noetherian property of local cohomology modules in several cases. Finally, we obtain a new characterization of the cohomological dimensions.
