The poset of normalized ideals of numerical semigroups with multiplicity three

TL;DR

This paper investigates the structure of normalized ideals in numerical semigroups with multiplicity three, proving the poset forms a lattice and distinguishing non-isomorphic posets for different semigroups.

Contribution

It establishes that the poset of normalized ideals is always a lattice for multiplicity three and differentiates between semigroups based on their poset structures.

Findings

The poset of normalized ideals is always a lattice.

Different semigroups with multiplicity three have non-isomorphic posets.

Provides structural insights into numerical semigroups with multiplicity three.

Abstract

We study the poset of normalized ideals of a numerical semigroup with multiplicity three. We show that this poset is always a lattice, and that two different numerical semigroups with multiplicity three have non-isomorphic posets of normalized ideals.