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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2312.06013 |
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| _version_ | 1866910568485486592 |
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| author | Colaço, Isabel Ojeda, Ignacio |
| author_facet | Colaço, Isabel Ojeda, Ignacio |
| contents | Let $\Bbbk$ be an arbitrary field and let $b > 1, n > 1$ and $a$ be three positive integers. In this paper we explicitly describe a minimal $S-$graded free resolution of the semigroup algebra $\Bbbk[S]$ when $S$ is a generalized repunit numerical semigroup, that is, when $S$ is the submonoid of $\mathbb{N}$ generated by $\{a_1, a_2, \ldots, a_n\}$ where $a_1 = \sum_{j=0}^{n-1} b^j$ and $a_i - a_{i-1} = a\, b^{i-2},\ i = 2, \ldots, n$, with $\gcd(a,a_1) = 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06013 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimal free resolution of generalized repunit algebras Colaço, Isabel Ojeda, Ignacio Commutative Algebra Primary: 16W50, 13D02 secondary: 20M14 Let $\Bbbk$ be an arbitrary field and let $b > 1, n > 1$ and $a$ be three positive integers. In this paper we explicitly describe a minimal $S-$graded free resolution of the semigroup algebra $\Bbbk[S]$ when $S$ is a generalized repunit numerical semigroup, that is, when $S$ is the submonoid of $\mathbb{N}$ generated by $\{a_1, a_2, \ldots, a_n\}$ where $a_1 = \sum_{j=0}^{n-1} b^j$ and $a_i - a_{i-1} = a\, b^{i-2},\ i = 2, \ldots, n$, with $\gcd(a,a_1) = 1$. |
| title | Minimal free resolution of generalized repunit algebras |
| topic | Commutative Algebra Primary: 16W50, 13D02 secondary: 20M14 |
| url | https://arxiv.org/abs/2312.06013 |