Remarks on effective uniform Briançon-Skoda
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914075752005632 |
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| author | Wheeler, Alexandria Zhang, Wenliang |
| author_facet | Wheeler, Alexandria Zhang, Wenliang |
| contents | Let $R$ be a noetherian commutative ring. Of great interest is the question whether one can find an explicit integer $k$ such that $\overline{I^{k+n}}\subseteq I^n$ for each ideal $I$ and each integer $n\geq 1$ (the notation $\overline{I^{k+n}}$ denotes the integral closure of $I^{k+n}$). In this article, we investigate this question and obtain optimal values of $k$ for $F$-pure (or dense $F$-pure type) rings and Cohen-Macaulay $F$-injective (or dense $F$-injective type) rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remarks on effective uniform Briançon-Skoda Wheeler, Alexandria Zhang, Wenliang Commutative Algebra Let $R$ be a noetherian commutative ring. Of great interest is the question whether one can find an explicit integer $k$ such that $\overline{I^{k+n}}\subseteq I^n$ for each ideal $I$ and each integer $n\geq 1$ (the notation $\overline{I^{k+n}}$ denotes the integral closure of $I^{k+n}$). In this article, we investigate this question and obtain optimal values of $k$ for $F$-pure (or dense $F$-pure type) rings and Cohen-Macaulay $F$-injective (or dense $F$-injective type) rings. |
| title | Remarks on effective uniform Briançon-Skoda |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2510.04004 |