The multiples of a numerical semigroup

Authors

IGNACIO OJEDAFollow
JOSÉ CARLOS ROSALESFollow

Author ORCID Identifier

IGNACIO OJEDA: 0000-0003-3173-5934

JOSÉ CARLOS ROSALES: 0000-0003-3353-4335

DOI

10.55730/1300-0098.3560

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.

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, IGNACIO and ROSALES, JOSÉ CARLOS (2024) "The multiples of a numerical semigroup," Turkish Journal of Mathematics: Vol. 48: No. 6, Article 5. https://doi.org/10.55730/1300-0098.3560
Available at: https://journals.tubitak.gov.tr/math/vol48/iss6/5