Research Specifications

Let a denote an ideal in a Noetherian ring R, and M a finitely generated R-module. We introduce the concept of the cohomological dimension filtration M = fMigc i=0, where c = cd(a;M) and Mi denotes the largest submodule of M such that cd(a;Mi)  i: Some properties of this filtration are investigated. In particular, if (R;m) is local and c = dimM, we are able to determine the annihilator of the top local cohomology module Hc a (M), namely AnnR(Hc a (M)) = AnnR(M=Mc􀀀1): As a consequence, there exists an ideal b of R such that AnnR(Hc a (M)) = AnnR(M=H0 b (M)). This generalizes the main results of Bahmanpour et al. (2012) and Lynch (2012).