On the Ratliff-Rush closure of an ideal of a one-dimensional ring
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911036481732608 |
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| author | Quinonez, Veronica Crispin D'Anna, Marco Micale, Vincenzo |
| author_facet | Quinonez, Veronica Crispin D'Anna, Marco Micale, Vincenzo |
| contents | 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 $h(I)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02444 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Ratliff-Rush closure of an ideal of a one-dimensional ring Quinonez, Veronica Crispin D'Anna, Marco Micale, Vincenzo Commutative Algebra 13A15, 13C13, 13H10, 20M12 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 $h(I)$. |
| title | On the Ratliff-Rush closure of an ideal of a one-dimensional ring |
| topic | Commutative Algebra 13A15, 13C13, 13H10, 20M12 |
| url | https://arxiv.org/abs/2507.02444 |