The strong uniform Artin-Rees property in codimension one

Details The strong uniform Artin-Rees property in codimension one The strong uniform Artin-Rees property in codimension one

1999-02-18

arxiv.org/abs/math/9902106v1

Mathematics

Commutative Algebra

14 pages, Latex

Scientific paper

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 $N\subset M$ be two finitely generated $A$-modules such that ${\rm dim}(M/N)\leq 1$. Then there exists an integer $s\geq 1$ such that, for all integers $n\geq s$ and for all ideals $I$ of $A$, $I^{n}M\cap N=I^{n-s}(I^{s}M\cap N)$.

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