The artinianness of formal local cohomology modules

Let I be an ideal of a commutative Noetherian local ring (R,m), M a finitely generated R-module and lim??nHim(M/InM) the i-th formal local cohomology module of M with respect to I. We prove some results concerning artinianness of lim??nHim(M/InM). We discuss the maximum and minimum integers such that lim??nHim(M/InM) is artinian.