JournalspmVol. 70 / No. 2DOI 10.4171/pm/1927

Rees quotients of numerical semigroups

  • Manuel Delgado

    Universidade do Porto, Portugal
  • Vítor H. Fernandes

    Universidade Nova de Lisboa, Caparica, Portugal
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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.