Proceedings of the American Mathematical Society

Symmetric numerical semigroups with arbitrary multiplicity and embedding dimension

Author(s): J. C. Rosales
Journal: Proc. Amer. Math. Soc. 129 (2001), 2197-2203.
MSC (2000): Primary 20M14, 20M05, 20M30, 13H10
Posted: January 17, 2001
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We construct symmetric numerical semigroups

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.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20M14, 20M05, 20M30, 13H10

J. C. Rosales
Affiliation: Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain
Email: jrosales@ugr.es

DOI: 10.1090/S0002-9939-01-05819-1
PII: S 0002-9939(01)05819-1
Keywords: Symmetric numerical semigroup, multiplicity, embedding dimension
Received by editor(s): July 29, 1999
Received by editor(s) in revised form: December 9, 1999
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

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