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

 

Every numerical semigroup is one half of a symmetric numerical semigroup


Authors: J. C. Rosales and P. A. García-Sánchez
Journal: Proc. Amer. Math. Soc. 136 (2008), 475-477
MSC (2000): Primary 20M14, 13H10
Published electronically: October 25, 2007
MathSciNet review: 2358486
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Abstract: Let $ S$ be a numerical semigroup. Then there exists a symmetric numerical semigroup $ \overline{S}$ such that $ S=\{ n\in \N ~\vert~ 2n \in \overline{S}\}$.


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Additional Information

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

P. A. García-Sánchez
Affiliation: Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain
Email: pedro@ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09098-3
PII: S 0002-9939(07)09098-3
Keywords: Numerical semigroup, symmetric numerical semigroup, Frobenius number
Received by editor(s): January 19, 2007
Published electronically: October 25, 2007
Additional Notes: The authors were supported by the project MTM2004-01446 and FEDER funds
The authors want to thank the referee for her/his comments and suggestions
Communicated by: Martin Lorenz
Article copyright: © Copyright 2007 American Mathematical Society