The multiples of a numerical semigroup
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914669863632896 |
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| author | Ojeda, Ignacio Rosales, José Carlos |
| author_facet | Ojeda, Ignacio Rosales, José Carlos |
| contents | Given two numerical semigroups $S$ and $T$ we say that $T$ is a multiple of $S$ if there exists an integer $d \in \mathbb{N} \setminus \{0\}$ such that $S = \{x \in \mathbb{N} \mid d x \in T\}$. In this paper we study the family of multiples of a (fixed) numerical semigroup. We also address the open problem of finding numerical semigroups of embedding dimension $e$ without any quotient of embedding dimension less than $e$, and provide new families with this property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04413 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The multiples of a numerical semigroup Ojeda, Ignacio Rosales, José Carlos Group Theory Primary: 20M14 Secondary: 05C05, 11D07 Given two numerical semigroups $S$ and $T$ we say that $T$ is a multiple of $S$ if there exists an integer $d \in \mathbb{N} \setminus \{0\}$ such that $S = \{x \in \mathbb{N} \mid d x \in T\}$. In this paper we study the family of multiples of a (fixed) numerical semigroup. We also address the open problem of finding numerical semigroups of embedding dimension $e$ without any quotient of embedding dimension less than $e$, and provide new families with this property. |
| title | The multiples of a numerical semigroup |
| topic | Group Theory Primary: 20M14 Secondary: 05C05, 11D07 |
| url | https://arxiv.org/abs/2402.04413 |