On numerical semigroups with high embedding dimension
type: Item
instance of: scholarly article
title: On numerical semigroups with high embedding dimension
zbMATH Open document ID: 0906.20042
published in: Journal of Algebra
publication date: 1998-10-26T00:00:00Z
review text: Let \(S\) be a numerical semigroup, that is, an additive submonoid of \(\mathbb{N}\) which generates \(\mathbb{Z}\) as a group. Let \(\{n_0<n_1<\cdots<n_p\}\) be a minimal system of generators for \(S\), let \(\varphi\colon\mathbb{N}^{p+1}\to\mathbb{N}\) be the semigroup homomorphism \(\varphi(a_0,a_1,\dots,a_p)=a_0n_0+a_1n_1+\cdots+a_pn_p\), and let \(\sigma\) be the kernel congruence of \(\varphi\). In this paper, the authors continue the investigation of the first-named author on the number of elements in a system of generators for \(\sigma\) with minimal cardinality. Specifically, they study the cases \(p=n_0-2\) and \(p=n_0-3\) for arbitrary numerical semigroups and the cases \(p=n_0-3\) and \(p=n_0-4\) for symmetric numerical semigroups.
reviewed by: David F. Anderson
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 1200011
zbMATH Keywords: minimal systems of generators
zbMATH Keywords: kernel congruences
zbMATH Keywords: numbers of elements
zbMATH Keywords: symmetric numerical semigroups
Wikidata QID: Q58843146
author: José Carlos Rosales
author: Pedro A. García Sánchez
MaRDI profile type: Publication
OpenAlex ID: W2064955121
cites work: Symmetric semigroups of integers generated by 4 elements
cites work: Generators and relations of abelian semigroups and semigroup rings
cites work: Q5343411
cites work: AN ALGORITHMIC METHOD TO COMPUTE A MINIMAL RELATION FOR ANY NUMERICAL SEMIGROUP
cites work: On numerical semigroups
cites work: On symmetric numerical semigroups
DOI: 10.1006/JABR.1997.7341
description: scientific article; zbMATH DE number 1200011