On the strong persistence property and normally torsion-freeness of square-free monomial ideals
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913582675918848 |
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| author | Bretto, Alain Nasernejad, Mehrdad Toledo, Jonathan |
| author_facet | Bretto, Alain Nasernejad, Mehrdad Toledo, Jonathan |
| contents | In this paper, we first show that any square-free monomial ideal in $K[x_1, x_2, x_3, x_4, x_5]$ has the strong persistence property. Next we will provide a criterion for a minimal counterexample to the Conforti-Cornuejols conjecture. Finally we give a necessary and sufficient condition to determine the normally torsion-freeness of a linear combination of two normally torsion-free square-free monomial ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the strong persistence property and normally torsion-freeness of square-free monomial ideals Bretto, Alain Nasernejad, Mehrdad Toledo, Jonathan Commutative Algebra In this paper, we first show that any square-free monomial ideal in $K[x_1, x_2, x_3, x_4, x_5]$ has the strong persistence property. Next we will provide a criterion for a minimal counterexample to the Conforti-Cornuejols conjecture. Finally we give a necessary and sufficient condition to determine the normally torsion-freeness of a linear combination of two normally torsion-free square-free monomial ideals. |
| title | On the strong persistence property and normally torsion-freeness of square-free monomial ideals |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2411.14227 |