On the Ratliff-Rush closure of an ideal of a one-dimensional ring

2025/07/03 by Quinonez, Veronica Crispin, D'Anna, Marco, Micale, Vincenzo
#13A15 #13C13 #13H10 #20M12 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.02444

Abstract

Let I be an ideal in a Noetherian ring R and let \widetildeI be its Ratliff-Rush closure. In this paper we study the asymptotic Ratliff-Rush number, i.e. h(I)=min\n∈\mathbb N₊ | I^m=\widetildeI^m, ∀ m≥ n\, in the one-dimensional case. Since 1≤ h(I)≤ r(I), where r(I) is the reduction number of I, we look for conditions that determine the extremal values of h(I).

Citations

• Tangent cones of monomial curves obtained by numerical duplication
• Notes on the behavior of the Ratliff-Rush filtration

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