When the poset of the ideal class monoid of a numerical semigroup is a lattice

TL;DR

This paper characterizes numerical semigroups whose ideal class monoid forms a lattice, analyzing the structure and irreducible elements of such lattices under various operations.

Contribution

It provides a characterization of when the ideal class monoid of a numerical semigroup is a lattice and studies its irreducible elements.

Findings

Identifies conditions under which the ideal class monoid is a lattice

Analyzes the irreducible elements with respect to union, intersection, infimum, and supremum

Provides structural insights into the lattice properties of ideal class monoids

Abstract

We characterize numerical semigroups for which the poset of its ideal class monoid is a lattice, and study the irreducible elements of such a lattice with respect to union, intersection, infimum and supremum.