Uniform annihilators of local cohomology

Abstract

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.