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Journal of the London Mathematical Society 2002 65(3):611-623; doi:10.1112/S0024610701003052
© 2002 by London Mathematical Society
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© The London Mathematical Society

Systems of Inequalities and Numerical Semigroups

J. C. Rosales, P. A. García-Sánchez, J. I. García-García and M. B. Branco

Departamento de Álgebra, Universidad de Granada E-18071 Granada, Spain, jrosales{at}ugr.es
Departamento de Álgebra, Universidad de Granada E-18071 Granada, Spain, pedro{at}ugr.es
Departamento de Álgebra, Universidad de Granada E-18071 Granada, Spain, jigg{at}ugr.es
Departamento de Matemática, Universidade de Évora 7000 Évora, Portugal, mbb{at}dmat.uevora.pt

Received 15 March 2001. Revision received 26 July 2001.

A one-to-one correspondence is described between the set S(m) of numerical semigroups with multiplicity m and the set of non-negative integer solutions of a system of linear Diophantine inequalities. This correspondence infers in S(m) a semigroup structure and the resulting semigroup is isomorphic to a subsemigroup of Nm–1. Finally, this result is particularized to the symmetric case.


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