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arXiv · 2412.00454

Positioned and primary positioned $\mathcal{C}$-semigroups

Carmelo Cisto·Raquel Tapia-Ramos
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Abstract

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 $k\in \mathcal{C}$.

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Carmelo Cisto, Raquel Tapia-Ramos. 2024-11-30. Positioned and primary positioned $\mathcal{C}$-semigroups. https://doi.org/10.1007/s10231-025-01634-4

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