Rees quotients of numerical semigroups

  • Manuel Delgado

    Universidade do Porto, Portugal
  • Vítor H. Fernandes

    Universidade Nova de Lisboa, Caparica, Portugal


We introduce a class of finite semigroups obtained by considering Rees quotients of numerical semigroups. Several natural questions concerning this class, as well as particular subclasses obtained by considering some special ideals, are answered while others remain open. We exhibit nice presentations for these semigroups and prove that the Rees quotients by ideals of , the positive integers under addition, constitute a set of generators for the pseudovariety of commutative and nilpotent semigroups.

Cite this article

Manuel Delgado, Vítor H. Fernandes, Rees quotients of numerical semigroups. Port. Math. 70 (2013), no. 2, pp. 93–112

DOI 10.4171/PM/1927