Abstract. Let a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. It is shown that AnnR(

Abstract. Let a denote an ideal in a commutative Noetherian ring R and M a finitely generated R-module. In this paper, we introduce the concept of the cohomological dimen-, where c = cd(a, M ) and M i denotes the largest submodule of M such that cd(a, M i ) ≤ i. Some properties of this filtration are investigated. In particular, in the case that (R, m) is local and c = dim M , we are able to determine the annihilator of the top local cohomology module H

Theorem 1.1. Let R be a Noetherian ring, a an ideal of R and M a non-zero finitely generated R-module such that cd(a, M) = c.

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