The strong uniform Artin-Rees property in codimension one
Abstract
The purpose of this paper is to prove the following theorem of uniform Artin-Rees properties: Let
A
be an excellent (in fact J-2) ring and let
N⊂M
be two finitely generated
A
-modules such that
dim(M/N)≤1
. Then there exists an integer
s≥1
such that, for all integers
n≥s
and for all ideals
I
of
A
,
I
n
M∩N=
I
n−s
(
I
s
M∩N)
.