  We prove that if M is a finitely-generated module of dimension d with finite
local cohomologies over a Noetherian local ring, and if the ith local
cohomology module of M is zero unless i = d, i = 0, and i = r for some r
strictly between 0 and d, then there is an integer l such that every parameter
ideal for M contained in the lth power of the maximal ideal has the same index
of reducibility on M. This theorem generalizes work of the second author
(math.AC/0408143) and is closely related to work of S. Goto, H. Sakurai
(math.AC/0306148), and N. Suzuki.
