Semigroup ideals and linear Diophantine equations
type: Item
instance of: scholarly article
title: Semigroup ideals and linear Diophantine equations
zbMATH Open document ID: 0939.20061
DOI: 10.1016/S0024-3795(99)00087-7
published in: Linear Algebra and its Applications
publication date: 1999-11-29T00:00:00Z
review text: Let \(S\) be a finitely generated commutative cancellative monoid, and let \(\{n_1,\dots,n_r\}\subset S\) be a set of generators for \(S\). Let \(k\) be a field, \(R=k[S]\) the associated semigroup \(k\)-algebra, \(R=k[X_1,\dots,X_r]\) the polynomial ring, and \(\varphi\colon R\to k[S]\) the \(k\)-algebra homomorphism given by \(\varphi(X_i)=n_i\). The author gives a purely algebraic algorithm to calculate a finite set of generators for \(\ker\varphi\). As an application, using Gröbner bases, an algorithm is given to determine whether a linear system of equations with integer coefficients having some of the equations in congruences admits non-negative integer solutions.
reviewed by: David F. Anderson
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 11D04
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 1371413
zbMATH Keywords: finitely generated commutative cancellative monoids
zbMATH Keywords: generators
zbMATH Keywords: semigroup algebras
zbMATH Keywords: algorithms
zbMATH Keywords: Gröbner bases
zbMATH Keywords: linear systems of equations
author: A. Vigneron-Tenorio
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1371413