Presentations of a numerical semigroup

  • J.C. Rosales
  • P.A. García-Sánchez
Part of the Developments in Mathematics book series (DEVM, volume 20)


Rédei in [53] shows that every congruence on ℕn is finitely generated. This result has since been known as Rédei’s theorem, and it is equivalent to the fact that every finitely generated (commutative) monoid is finitely presented. Rédei’s proof is long and elaborated. Many other authors have given alternative and much simpler proofs than his (see for instance [31, 39, 41, 56]). Since numerical semigroups are cancellative monoids, a different approach can be chosen to prove Rédei’s theorem. And this is precisely the path we choose in this chapter.


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Algebra, Faculty of SciencesUniversity of Granada, Campus University FuentenuevaGranadaSpain

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