On normal affine semigroups
type: Item
instance of: scholarly article
title: On normal affine semigroups
zbMATH Open document ID: 0943.20062
DOI: 10.1016/S0024-3795(98)10152-0
published in: Linear Algebra and its Applications
publication date: 2000-02-17T00:00:00Z
review text: Let \(S\) be an affine semigroup, i.e., a finitely generated additive submonoid of \(\mathbb{N}^k\). Then \(S\) is said to be normal if \(ng\in S\) implies \(g\in S\), where \(n\geq 1\) is an integer and \(g\in G(S)\), the group generated by \(S\). In this paper, the authors develop algorithms to (1) check, from the generators of an affine semigroup, whether the semigroup is normal, and (2) determine, from a finite presentation of a semigroup, whether the semigroup is affine and normal. Applications are also given for computing the nonnegative integer solutions to a system of linear equations with rational coefficients, determining whether a semigroup ring is Gorenstein, and computing the dual of a semigroup.
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M25
zbMATH DE Number: 1331731
zbMATH Keywords: normal semigroups
zbMATH Keywords: affine semigroups
zbMATH Keywords: generators
zbMATH Keywords: finite presentations
zbMATH Keywords: systems of linear equations
zbMATH Keywords: semigroup rings
author: José Carlos Rosales
author: Pedro A. García Sánchez
reviewed by: David F. Anderson
Wikidata QID: Q58843103
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1331731