Annihilator of top local cohomology and Lynch's conjecture.

Let R be a commutative Noetherian ring, a proper ideal of R and N a nonzero finitely generated R -module with N ≠ N. Let d (respectively, c) be the smallest (respectively, greatest) non-negative integer i such that the local cohomology H i (N) is nonzero. In this paper, we provide sharp bounds under inclusion for the annihilators of the local cohomology modules H d (N) , H c (N) and these annihilators are computed in certain cases. Also, we construct a counterexample to Lynch's conjecture. [ABSTRACT FROM AUTHOR]