Some results on Artinian cofinite top local cohomology modules

Let (R, m) be a Noetherian local ring, I be an ideal of R, and M be a finitely generated R-module such that H-I(t) (M) is Artinian and I-cofinite, where t = cd(I, M). In this paper, we give some equivalent conditions for the property Ann R (0: (HIt (M)) p) = p for all prime ideals p superset of Ann RHIt (M). (*) Also, we show that if H-I(t) (M) satisfies the property (*), then H-I(t) (M) congruent to H-m(t)(M/N) for some submodule N of M with dim (M/N) = t.