Positioned and primary positioned $\mathcal{C}$-semigroups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914281823404032 |
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| author | Cisto, Carmelo Tapia-Ramos, Raquel |
| author_facet | Cisto, Carmelo Tapia-Ramos, Raquel |
| contents | Let $\mathcal{C}$ be a positive integer cone and $k\in \mathcal{C}$. A $\mathcal{C}$-semigroup $S$ is $k$-positioned if for every $h\in \mathcal{C}\setminus S$ we have that $k-h$ belongs to $S$. In this work, we focus on this family of semigroups and introduce primary positioned $\mathcal{C}$-semigroups, characterizing a subfamily of them through the perspective of irreducibility. Furthermore, we provide some procedures to compute all such semigroups, describing a family of graphs containing all the primary positioned $\mathcal{C}$-semigroups for a fixed $k\in \mathcal{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00454 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positioned and primary positioned $\mathcal{C}$-semigroups Cisto, Carmelo Tapia-Ramos, Raquel Combinatorics Commutative Algebra 20M14, 06F05, 05C05, 11D07 Let $\mathcal{C}$ be a positive integer cone and $k\in \mathcal{C}$. A $\mathcal{C}$-semigroup $S$ is $k$-positioned if for every $h\in \mathcal{C}\setminus S$ we have that $k-h$ belongs to $S$. In this work, we focus on this family of semigroups and introduce primary positioned $\mathcal{C}$-semigroups, characterizing a subfamily of them through the perspective of irreducibility. Furthermore, we provide some procedures to compute all such semigroups, describing a family of graphs containing all the primary positioned $\mathcal{C}$-semigroups for a fixed $k\in \mathcal{C}$. |
| title | Positioned and primary positioned $\mathcal{C}$-semigroups |
| topic | Combinatorics Commutative Algebra 20M14, 06F05, 05C05, 11D07 |
| url | https://arxiv.org/abs/2412.00454 |