Turkish Journal of Mathematics
Abstract
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.
DOI
10.55730/1300-0098.3560
Keywords
Numerical semigroup, monoids, quotient of a numerical semigroup, irreducible numerical semigroups, rooted tree
First Page
1055
Last Page
1066
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
OJEDA, I, & ROSALES, J (2024). The multiples of a numerical semigroup. Turkish Journal of Mathematics 48 (6): 1055-1066. https://doi.org/10.55730/1300-0098.3560
