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Bulletin of the London Mathematical Society Advance Access originally published online on April 12, 2008
Bulletin of the London Mathematical Society 2008 40(2):347-352; doi:10.1112/blms/bdn010
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© 2008 London Mathematical Society

One half of a pseudo-symmetric numerical semigroup

J. C. Rosales

Departamento de Álgebra
Universidad de Granada
E-18071 Granada
Spain

Received 30 September 2007. Revision received 19 October 2007.

We prove that a numerical semigroup is irreducible if and only if it is one half of a pseudo-symmetric numerical semigroup. As a consequence we find that every numerical semigroup can be obtained by dividing a pseudo-symmetric numerical semigroup by 4.

The author is supported by the project MTM2004-01446 and FEDER funds. The author wants to thank P. A. García-Sánchez, P. Vasco and the referee for his comments and suggestions.

2000 Mathematics Subject Classification 20M14, 13H10.


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