Location: Science Conference Room / Zouk Campus
Time: Noon
Speaker: Dr. Aline Hosry
Affiliation: LU
Abstract: Let R be a Noetherian ring and let N⊆ M be finitely generated R-modules. For an ideal I ⊆R, the classical Artin-Rees Lemma states that there exists an integer h, depending on the ideal I and the inclusion N⊆ M, such that
I^n M ∩N ⊆ I^(n-h) N, for all n ≥h.
Eisenbud and Huneke asked if, given a local ring (R,m) and a finitely generated R-module M, there exists a uniform Artin-Rees number, i.e., an integer h such that for all ideals I and all syzygies of M, N ⊆F (where F is free), we have I^n F ∩N ⊆ I^(n-h) N, for all n ≥h. They proved some cases where this occurs, and Striuli proved the result when the ring is Noetherian local of dimension one or two. We will outline how a much more general result holds.