Portugaliae Mathematica


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Volume 70, Issue 2, 2013, pp. 93–112
DOI: 10.4171/PM/1927

Published online: 2013-08-02

Rees quotients of numerical semigroups

Manuel Delgado[1] and Vítor H. Fernandes[2]

(1) Universidade do Porto, Portugal
(2) 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 $\mathbb{N}$, the positive integers under addition, constitute a set of generators for the pseudovariety of commutative and nilpotent semigroups.

Keywords: Numerical semigroups, finite semigroups, Rees quotients

Delgado Manuel, Fernandes Vítor: Rees quotients of numerical semigroups. Port. Math. 70 (2013), 93-112. doi: 10.4171/PM/1927