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SYSTEMS OF INEQUALITIES AND NUMERICAL SEMIGROUPS

Published online by Cambridge University Press:  24 March 2003

J. C. ROSALES ,
P. A. GARCÍA-SÁNCHEZ ,
J. I. GARCÍA-GARCÍA  and
M. B. BRANCO
J. C. ROSALES
Affiliation:
Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spainjrosales@ugr.espedro@ugr.esjigg@ugr.es
P. A. GARCÍA-SÁNCHEZ
Affiliation:
Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spainjrosales@ugr.espedro@ugr.esjigg@ugr.es
J. I. GARCÍA-GARCÍA
Affiliation:
Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spainjrosales@ugr.espedro@ugr.esjigg@ugr.es
M. B. BRANCO
Affiliation:
Departamento de Matemática, Universidade de Évora, 7000 Évora, Portugalmbb@dmat.uevora.pt
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Abstract

A one-to-one correspondence is described between the set ${\cal J}(m)$ of numerical semigroups with multiplicity $m$ and the set of non-negative integer solutions of a system of linear Diophantine inequalities. This correspondence infers in ${\cal J}(m)$ a semigroup structure and the resulting semigroup is isomorphic to a subsemigroup of ${\bb N}^{m-1}$ . Finally, this result is particularized to the symmetric case.

Information

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 611 - 623
Copyright
The London Mathematical Society, 2002

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Footnotes

This paper was supported by the project BFM2000-1469.