On the normally torsion-freeness of square-free monomial ideals
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909179581562880 |
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| author | Nasernejad, Mehrdad Quiñonez, Veronica Crispin Hochstättler, Winfried |
| author_facet | Nasernejad, Mehrdad Quiñonez, Veronica Crispin Hochstättler, Winfried |
| contents | Let $I\subset R=K[x_1, \ldots, x_n]$ be a square-free monomial ideal, $\mathfrak{q}$ be a prime monomial ideal in $R$, $h$ be a square-free monomial in $R$ with $\mathrm{supp}(h) \cap (\mathrm{supp}(\mathfrak{q}) \cup \mathrm{supp}(I))=\emptyset$, and $L:=I\cap (\mathfrak{q}, h)$. In this paper, we first focus on the associated primes of powers of $L$ and explore the normally torsion-freeness of $L$. We also give an application on a comb inatorial result. Next, we study when a square-free monomial ideal is minimally not normally torsion-free. Particularly, we introduce a class of square-free monomial ideals, which are minimally not normally torsion-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11850 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the normally torsion-freeness of square-free monomial ideals Nasernejad, Mehrdad Quiñonez, Veronica Crispin Hochstättler, Winfried Commutative Algebra 13B25 Let $I\subset R=K[x_1, \ldots, x_n]$ be a square-free monomial ideal, $\mathfrak{q}$ be a prime monomial ideal in $R$, $h$ be a square-free monomial in $R$ with $\mathrm{supp}(h) \cap (\mathrm{supp}(\mathfrak{q}) \cup \mathrm{supp}(I))=\emptyset$, and $L:=I\cap (\mathfrak{q}, h)$. In this paper, we first focus on the associated primes of powers of $L$ and explore the normally torsion-freeness of $L$. We also give an application on a comb inatorial result. Next, we study when a square-free monomial ideal is minimally not normally torsion-free. Particularly, we introduce a class of square-free monomial ideals, which are minimally not normally torsion-free. |
| title | On the normally torsion-freeness of square-free monomial ideals |
| topic | Commutative Algebra 13B25 |
| url | https://arxiv.org/abs/2311.11850 |