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Presentations of a numerical semigroup

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Part of the Developments in Mathematics book series (DEVM,volume 20)

Abstract

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.

Keywords

  • Binary Relation
  • Numerical Semigroup
  • Minimal Relation
  • Free Monoids
  • Cancellative Monoids

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to J.C. Rosales .

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Rosales, J., García-Sánchez, P. (2009). Presentations of a numerical semigroup. In: Numerical Semigroups. Developments in Mathematics, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0160-6_8

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