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Systems of proportionally modular Diophantine inequalities

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Abstract

The set of integer solutions to the inequality ax mod b≤c x is a numerical semigroup. We study numerical semigroups that are intersections of these numerical semigroups. Recently it has been shown that this class of numerical semigroups coincides with the class of numerical semigroups having a Toms decomposition.

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Authors and Affiliations

  1. Departamento de Matemática Pura, Faculdade de Ciências, 4169-007, Porto, Portugal

    M. Delgado

  2. Departamento de Álgebra, Universidad de Granada, 18071, Granada, Spain

    P. A. García-Sánchez, J. C. Rosales & J. M. Urbano-Blanco

Authors
  1. M. Delgado
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  2. P. A. García-Sánchez
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  3. J. C. Rosales
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  4. J. M. Urbano-Blanco
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Corresponding author

Correspondence to M. Delgado.

Additional information

Communicated by Benjamin Steinberg.

The first author was (partially) supported by the Centro de Matemática da Universidade do Porto (CMUP), financed by FCT (Portugal) through the programmes POCTI and POSI, with national and European Community structural funds.

The last three authors are supported by the project MTM2004-01446 and FEDER funds.

The authors would like to thank the referee for her/his comments and suggestions.

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Delgado, M., García-Sánchez, P.A., Rosales, J.C. et al. Systems of proportionally modular Diophantine inequalities. Semigroup Forum 76, 469–488 (2008). https://doi.org/10.1007/s00233-008-9049-5

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  • DOI: https://doi.org/10.1007/s00233-008-9049-5

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