A remark on sequentially Cohen-Macaulay monomial ideals
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909207967563776 |
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| author | Koolani, Mozhgan Mafi, Amir |
| author_facet | Koolani, Mozhgan Mafi, Amir |
| contents | Let $R=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. We show that if $G$ is a connected graph with a basic $5$-cycle $C$, then $G$ is a sequentially Cohen-Macaulay graph if and only if there exists a shedding vertex $x$ of $C$ such that $G\setminus x$ and $G\setminus N[x]$ are sequentially Cohen-Macaulay graphs. Furthermore, we study the sequentially Cohen-Macaulay and Castelnuovo-Mumford regularity of square-free monomial ideals in some special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04979 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A remark on sequentially Cohen-Macaulay monomial ideals Koolani, Mozhgan Mafi, Amir Commutative Algebra 13C14, 13F55, 05E45 Let $R=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. We show that if $G$ is a connected graph with a basic $5$-cycle $C$, then $G$ is a sequentially Cohen-Macaulay graph if and only if there exists a shedding vertex $x$ of $C$ such that $G\setminus x$ and $G\setminus N[x]$ are sequentially Cohen-Macaulay graphs. Furthermore, we study the sequentially Cohen-Macaulay and Castelnuovo-Mumford regularity of square-free monomial ideals in some special cases. |
| title | A remark on sequentially Cohen-Macaulay monomial ideals |
| topic | Commutative Algebra 13C14, 13F55, 05E45 |
| url | https://arxiv.org/abs/2308.04979 |