The regularity of monomial ideals and their integral closures
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.
Authors
- Guangjun Zhu (ORCID: https://orcid.org/0000-0002-7196-1090)
- Cheng Gong (ORCID: https://orcid.org/0000-0002-1527-7366)
- Yijun Cui (ORCID: https://orcid.org/0000-0001-5716-6499)
Publication Details
- Journal
- Czechoslovak Mathematical Journal
- Published
- 2026-10-28
- DOI
- https://doi.org/10.21136/cmj.2026.0360-25
- Primary Topic
- Commutative Algebra and Its Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- Government of Jiangsu Province
- Natural Science Foundation of Jiangsu Province