The oversemigroups of a numerical semigroup.
type: Item
instance of: scholarly article
title: The oversemigroups of a numerical semigroup.
zbMATH Open document ID: 1043.20034
author: J. A. Jiménez Madrid
author: José Carlos Rosales
author: Pedro A. García Sánchez
author: J. I. García-García
published in: Semigroup Forum
publication date: 2003-08-31T00:00:00Z
review text: A numerical semigroup \(S\) is an additive submonoid of the set \(\mathbb{N}\) of nonnegative integers such that \(\mathbb{N}-S\) is finite. A numerical semigroup is said to be irreducible if it cannot be expressed as an intersection of two numerical semigroups properly containing it. It is known that every numerical semigroup is the intersection of finitely many irreducible numerical semigroups. In this paper, the authors study the set of numerical semigroups containing a given numerical semigroup and as applications give several characterizations of irreducible numerical semigroups. These results are then used to give an algorithmic method for constructing a minimal (with respect to the number of irreducible semigroups) decompositon of any numerical semigroup as an intersection of irreducible numerical semigroups.
Mathematics Subject Classification ID: 20M14
zbMATH DE Number: 1972517
zbMATH Keywords: numerical semigroups
zbMATH Keywords: intersections of irreducible semigroups
reviewed by: David F. Anderson
describes a project that uses: NumericalSemigroupsWithGenus
MaRDI profile type: Publication
Wikidata QID: Q58842970
full work available at URL: s00233-002-0007-3
OpenAlex ID: W2147044958
DOI: 10.1007/S00233-002-0007-3
description: scientific article; zbMATH DE number 1972517