IRREDUCIBLE NUMERICAL SEMIGROUPS - Branco, Manuel B. (2008)
We give a characterization for irreducible numerical semigroups. From this characterization we obtain that every irreducible numerical semigroup is either a symmetric or pseudosymmetric numerical semigroup. We study the minimal presentations of an irreducible numerical semigroup. Separately, we deal with the cases of maximal embedding dimension and multiplicity 3 and 4.