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Symmetric numerical semigroups with arbitrary multiplicity and embedding dimension

Author: J. C. Rosales
Journal: Proc. Amer. Math. Soc. 129 (2001), 2197-2203
MSC (2000): Primary 20M14, 20M05, 20M30, 13H10
Published electronically: January 17, 2001
MathSciNet review: 1823900
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We construct symmetric numerical semigroups $S$ for every minimal number of generators $\mu(S)$ and multiplicity $\mathsf{m}(S)$, $2\leq \mu(S)\leq \mathsf{m}(S)-1$. Furthermore we show that the set of their defining congruence is minimally generated by $\mu(S)(\mu(S)-1)/2-1$ elements.

References [Enhancements On Off] (What's this?)

  • 1. V. Barucci, D. E. Dobbs and M. Fontana, ``Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analyticalle Irreducible Local Domains'', Memoirs of the Amer. Math. Soc. 125(1997). MR 97g:13039
  • 2. H. Bresinsky, On prime ideal with generic zero $x_i=t^{n_i}$, Proc. Amer. Math. Soc. 47(1975) 329-332. MR 52:10741
  • 3. H. Bresinsky, Symmetric semigroups of integers generated by $4$ elements, Manuscripta Math. 17(1975) 205-219. MR 54:2660
  • 4. J. Herzog, Generators and relations of abelian semigroups and semigroup rings, Manuscripta Math. 3(1970), 175-193. MR 42:4657
  • 5. E. Kunz, The value semigroup of an one dimensional Gorenstein ring, Proc. Amer. Math. Soc. 25(1970), 748-751. MR 42:263
  • 6. L. Rédei, ``The theory of finitely generated commutative semigroups.'' Pergamon, Oxford-Edinburgh-New York, 1965. MR 32:5761
  • 7. J. C. Rosales and P. A. García-Sánchez, ``Finitely generated commutative monoids'', Nova Science Publishers, NewYork, 1999. MR 2000d:20074
  • 8. J. C. Rosales, An algorithm for determining a minimal relation associated to a numerical semigroup, Int. J. Algebra and Comput. 6(1996), 441-455. MR 97f:20080
  • 9. J. C. Rosales, On symmetric numerical semigroups, J. Algebra 182(1996), 422-434. MR 98h:20099
  • 10. J. C. Rosales and P. A. García-Sánchez, On numerical semigroups with high embedding dimension, J. Algebra 203(1998), 567-578. MR 99g:20108
  • 11. J. C. Rosales, Numerical Semigroups with Apéry sets of unique expression, J. Algebra 226 (2000), 479-487.

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Additional Information

J. C. Rosales
Affiliation: Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain

Keywords: Symmetric numerical semigroup, multiplicity, embedding dimension
Received by editor(s): July 29, 1999
Received by editor(s) in revised form: December 9, 1999
Published electronically: January 17, 2001
Additional Notes: This paper was supported by the project DGES PB96-1424.
The author would like to thank P. A. García-Sánchez, J. I. García-García and the referee for their comments and suggestions.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2001 American Mathematical Society

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