Let I be an ideal of a commutative Noetherian ring R. We determine the set of all attached primes of the top local cohomology module of any finitely generated R-module M with respect to the ideal I of R in terms of certain elements of Supp M. Then as a consequence of this result we show that for any pair of finitely generated R-modules M and N with Supp N ⊆ Supp M, if cd(I, M) = cd(I, N) = c ≥ 0, then AttRHc I (N) ⊆ AttRHc I (M) and Rad(AnnRHc I (M)) ⊆ Rad(AnnRHc I (N)). Furthermore, in the case that R is a local ring, we prove some similar results concerning the associated primes of Matlis dual functors of top local cohomology modules
