Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids

TL;DR

This paper investigates arithmetical invariants in atomic monoids using semigroup theory, providing new characterizations and applying them to numerical and Krull monoids to understand factorization non-uniqueness.

Contribution

It introduces semigroup-theoretical characterizations of arithmetical invariants and applies these to numerical and Krull monoids, advancing the understanding of their factorization properties.

Findings

Characterizations of arithmetical invariants via monoid of relations

Applications to numerical monoids and Krull monoids

Insights into non-unique factorizations

Abstract

Arithmetical invariants---such as sets of lengths, catenary and tame degrees---describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.