The strong uniform Artin-Rees property in codimension one
نویسنده
چکیده
This result is a variation of a theorem of Duncan and O’Carroll [DO]: maximal ideals are replaced for any ideal using the unavoidable hypothesis dim(M/N) ≤ 1 (as an Example of Wang shows [W1]). Moreover it provides a partial positive answer to the question raised by Huneke in Conjecture 1.3 [H1]. We begin by recalling what is called uniform Artin-Rees properties. Let A be a noetherian ring, I be an ideal of A and let N ⊆M be two finitely generated A-modules. The usual Artin-Rees lemma states that there exists an integer s ≥ 1, depending on N , M and I, such that for all n ≥ s,
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