Every positive integer is the Frobenius number of an irreducible numerical semigroup with at most four generators.
type: Item
instance of: scholarly article
title: Every positive integer is the Frobenius number of an irreducible numerical semigroup with at most four generators.
zbMATH Open document ID: 1059.20059
DOI: 10.1007/BF02385481
author: Pedro A. García Sánchez
author: José Carlos Rosales
published in: Arkiv för Matematik
publication date: 2004-09-28T00:00:00Z
review text: The Frobenius number \(g(S)\) of a numerical semigroup \(S\) is the maximum of the set \(\mathbb{N}\setminus S\). A (numerical) semigroup is irreducible if it cannot be expressed as the intersection of two numerical semigroups properly containing it. Irreducible semigroups are closely related to symmetric and pseudo-symmetric ones. The interest in these types of semigroups comes from ring theory, since they provide Gorenstein and Kunz semigroup rings. For any positive integer \(g\), the authors give an easy method to get irreducible semigroups of Frobenius number \(g\). These semigroups have at most four generators, being that the least number of generators needed for the general case.
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 11D07
zbMATH DE Number: 2103850
zbMATH Keywords: Frobenius numbers
zbMATH Keywords: irreducible numerical semigroups
zbMATH Keywords: intersections of numerical semigroups
zbMATH Keywords: numbers of generators
Wikidata QID: Q58842902
reviewed by: Carlos Galindo
describes a project that uses: NumericalSemigroupsWithGenus
MaRDI profile type: Publication
cites work: Q5837528
cites work: Maximality properties in numerical semigroups and applications to one-dimensional analytically irreducible local domains
cites work: On formulas for the Frobenius number of a numerical semigroup.
cites work: On numerical semigroups
cites work: Numerical semigroups that can be expressed as an intersection of symmetric numerical semigroups
cites work: Decomposition of a numerical semigroup as an intersection of irreducible numerical semigroups.
cites work: Irreducible numerical semigroups.
cites work: The oversemigroups of a numerical semigroup.
description: scientific article; zbMATH DE number 2103850