  In this paper, we study the properties of noetherian rings with uniform
annihilators. It turns out that all these rings should be universally catenary
and locally equidimensional. We will give a necessary and sufficient condition
for these rings, which enable us to prove that if a ring R is the image of a
Cohen-Macaulay ring of finite dimension, then R has a uniform annihilator of
local cohomology. Moreover, we will give a positive answer to the conjecture
[Hu, Conjecture 2.13] about the excellent rings with dimension no more than 5.
