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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Abstract | References | Similar Articles | Additional Information

Abstract:

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.


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Additional Information

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

DOI: http://dx.doi.org/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
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