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. $h(I)=\min\{ n\in\mathbb N_+ \mid I^m=\widetilde{ I^m}, \ \forall \ m\ge n\}$, 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 $h(I)$.
Categories: math.AC