Pseudo-Frobenius numbers and defining ideals in stretched numerical semigroup rings
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| Format: | Preprint |
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2025
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| _version_ | 1866910782461050880 |
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| author | Van Kien, Do Matsuoka, Naoyuki Ozaki, Taiga |
| author_facet | Van Kien, Do Matsuoka, Naoyuki Ozaki, Taiga |
| contents | The pseudo-Frobenius numbers of a numerical semigroup $H$ are deeply connected to the structure of the defining ideal of its semigroup ring $k[H]$. In this paper, we resolve a certain conjecture related to this connection under the assumption that $k[H]/(t^a)$ is stretched, where $a$ is the multiplicity of $H$. Furthermore, we provide numerical conditions for the tangent cone of $k[H]$ to be Cohen-Macaulay. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_06415 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pseudo-Frobenius numbers and defining ideals in stretched numerical semigroup rings Van Kien, Do Matsuoka, Naoyuki Ozaki, Taiga Commutative Algebra 13D02, 13A02, 13A30, 13G05, 20M25 The pseudo-Frobenius numbers of a numerical semigroup $H$ are deeply connected to the structure of the defining ideal of its semigroup ring $k[H]$. In this paper, we resolve a certain conjecture related to this connection under the assumption that $k[H]/(t^a)$ is stretched, where $a$ is the multiplicity of $H$. Furthermore, we provide numerical conditions for the tangent cone of $k[H]$ to be Cohen-Macaulay. |
| title | Pseudo-Frobenius numbers and defining ideals in stretched numerical semigroup rings |
| topic | Commutative Algebra 13D02, 13A02, 13A30, 13G05, 20M25 |
| url | https://arxiv.org/abs/2501.06415 |