Families of numerical semigroups and a special case of the Huneke-Wiegand conjecture
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911845764300800 |
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| author | Landeros, Miguel O'Neill, Christopher Pelayo, Roberto Peña, Karina Ren, James Wissman, Brian |
| author_facet | Landeros, Miguel O'Neill, Christopher Pelayo, Roberto Peña, Karina Ren, James Wissman, Brian |
| contents | The Huneke-Wiegand conjecture is a decades-long open question in commutative algebra. García-Sánchez and Leamer showed that a special case of this conjecture concerning numerical semigroup rings $\Bbbk[Γ]$ can be answered in the affirmative by locating certain arithmetic sequences within the numerical semigroup $Γ$. In this paper, we use their approach to prove the Huneke-Wiegand conjecture in the case where $Γ$ is generated by a generalized arithmetic sequence and showcase how visualizations can be leveraged to find the requisite arithmetic sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12519 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Families of numerical semigroups and a special case of the Huneke-Wiegand conjecture Landeros, Miguel O'Neill, Christopher Pelayo, Roberto Peña, Karina Ren, James Wissman, Brian Commutative Algebra The Huneke-Wiegand conjecture is a decades-long open question in commutative algebra. García-Sánchez and Leamer showed that a special case of this conjecture concerning numerical semigroup rings $\Bbbk[Γ]$ can be answered in the affirmative by locating certain arithmetic sequences within the numerical semigroup $Γ$. In this paper, we use their approach to prove the Huneke-Wiegand conjecture in the case where $Γ$ is generated by a generalized arithmetic sequence and showcase how visualizations can be leveraged to find the requisite arithmetic sequences. |
| title | Families of numerical semigroups and a special case of the Huneke-Wiegand conjecture |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2404.12519 |