Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, first online, pp. 1-22

The regularity of monomial ideals and their integral closures

Yijun CUI, Cheng GONG, Guangjun ZHU

Received September 19, 2025. Published online October 28, 2026.

Abstract: Let $I$ be a monomial ideal in a polynomial ring $S=\mathbb K[x_1,\ldots,x_n]$ over a field $\mathbb K$ with $n=2$ or $3$, and let $\overline{I}$ be its integral closure. We will show that ${\rm reg}(\overline{I}) \le{\rm reg}(I)$. Furthermore, if $I$ is generated by monomials of degree $d$, then ${\rm reg}(I)=d$ if and only if $I$ has linear quotients.

Keywords: regularity; monomial ideal; integral closure; linear quotient

Classification MSC: 13F20, 13C05, 13D02

DOI: 10.21136/CMJ.2026.0360-25

PDF available at: Springer Institute of Mathematics CAS

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Affiliations: Yijun Cui (corresponding author), Cheng Gong, Guangjun Zhu, Soochow University, 50 E Ring Rd, Gusu District, Suzhou, Jiangsu, 215006, P. R. China, e-mail: 237546805@qq.com, cgong@suda.edu.cn, zhuguangjun@suda.edu.cn

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