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On the Ratliff-Rush closure of an ideal of a one-dimensional ring (2507.02444v1)
Published 3 Jul 2025 in math.AC
Abstract: Let $I$ be an ideal in a Noetherian ring $R$ and let $\widetilde{I}$ be its Ratliff-Rush closure. In this paper we study the asymptotic Ratliff-Rush number, i.e. $h(I)=\min{n\in\mathbb N_+ \mid Im=\widetilde{Im}, \ \forall \ m\ge n}$, in the one-dimensional case. Since $1\le h(I)\le r(I)$, where $r(I)$ is the reduction number of $I$, we look for conditions that determine the extremal values of $h(I)$.
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