The regularity of monomial ideals and their integral closures
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911484142944256 |
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| author | Cui, Yijun Gong, Cheng Zhu, Guangjun |
| author_facet | Cui, Yijun Gong, Cheng Zhu, Guangjun |
| contents | Let $I$ be a monomial ideal in a polynomial ring $S=K[x_1,\ldots,x_n]$ over a field $K$ with $n=2$ or $3$, and let $\overline{I}$ be its integral closure. We will show that $\text{reg} (\overline{I}) \le \text{reg} (I)$. Furthermore, if $I$ is generated by elements of degree $d$, then $\text{reg} (I)=d$ if and only if $I$ has linear quotients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The regularity of monomial ideals and their integral closures Cui, Yijun Gong, Cheng Zhu, Guangjun Commutative Algebra Let $I$ be a monomial ideal in a polynomial ring $S=K[x_1,\ldots,x_n]$ over a field $K$ with $n=2$ or $3$, and let $\overline{I}$ be its integral closure. We will show that $\text{reg} (\overline{I}) \le \text{reg} (I)$. Furthermore, if $I$ is generated by elements of degree $d$, then $\text{reg} (I)=d$ if and only if $I$ has linear quotients. |
| title | The regularity of monomial ideals and their integral closures |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2509.15119 |