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Every numerical semigroup is one half of a symmetric numerical semigroup

Author(s): J. C. Rosales; P. A. García-Sánchez
Journal: Proc. Amer. Math. Soc. 136 (2008), 475-477.
MSC (2000): Primary 20M14, 13H10
Posted: October 25, 2007
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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}\}$.

References:

1.
J. L. Ramírez Alfonsín, The Diophantine Frobenius problem, Oxford Lecture Series in Mathematics and Its Applications, 30. Oxford University Press, Oxford, 2005. MR 02260521 (2007i:11052)

2.
E. Kunz, The value semigroup of one dimensional Gorenstein ring, Proc. Amer. Math. Soc. 25 (1970), 748-751. MR 0265353 (42:263)

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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: 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
Posted: 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
Copyright of article: Copyright 2007, American Mathematical Society

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