Several Properties Of Uniform Local Cohomology Nullifiers

The existence of uniform local cohomological annihilators has many applications in the commutative algebra.It is related to a series of works such as the existence big Cohen-Macaulay algebras and an uniform Artin-Rees theorem.The main purpose of this paper is to study the existence of uniform local cohomology annihilators of finitely generated algebras over a ring R with an uniform local cohomology annihilator.We obtain the following results:1)if(R,m)is a local ring with an uniform local cohomological annihilator x,we will prove that there is a positive integer n such that for every I=(x1,…,xd)generated by a system of parameters,xn is an uniform local cohomological annihilator for the Rees algebra R[x1/xi,…,xd-1/xi].2)We will prove that if an uniform local cohomological annihilator x of a Noetherian ring R is not contained in a prime ideal p,then there is an uniform local cohomological annihilator in R/p.In particular,for any ideal I of R which is not in any minimal prime ideal or is nilpotent,the Rees algebra R[tI] has such local cohomological annihilator.