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(∆) = {I ∪{0}: I is an ideal of ∆} is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set Ja(∆) = {S ϵ J(∆): Max(∆\S) = a} for a given a ϵ ∆. As a consequence, we obtain another algorithm that computes all the elements of J(∆) with a fixed genus.