The lattice of ideals of a numerical semigroup and its Frobenius restricted variety associated

Abstract

Let be a numerical semigroup. In this work we show that J (Δ) = {I ∪ {0}: I is an ideal of Δ} is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set Ja(Δ) = {S ∈ J (Δ) : max(Δ\S) = a} for a given a ∈ Δ. As a consequence, we obtain another algorithm that computes all the elements of J (Δ) with a fixed genus.