The oversemigroups of a numerical semigroup. (Q1402913)

A numerical semigroup \(S\) is an additive submonoid of the set \(\mathbb{N}\) of nonnegative integers such that \(\mathbb{N}-S\) is finite. A numerical semigroup is said to be irreducible if it cannot be expressed as an intersection of two numerical semigroups properly containing it. It is known that every numerical semigroup is the intersection of finitely many irreducible numerical semigroups. In this paper, the authors study the set of numerical semigroups containing a given numerical semigroup and as applications give several characterizations of irreducible numerical semigroups. These results are then used to give an algorithmic method for constructing a minimal (with respect to the number of irreducible semigroups) decompositon of any numerical semigroup as an intersection of irreducible numerical semigroups.