# A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions

## TL;DR

This paper characterizes the class groups of Krull monoids where all sets of lengths form (almost) arithmetical progressions, using additive combinatorics to identify the structural conditions involved.

## Contribution

It provides a new characterization of class groups ensuring sets of lengths are (almost) arithmetical progressions in Krull monoids.

## Key findings

- Sets of lengths depend solely on the class group G.
- Characterization of G where sets of lengths are (almost) arithmetical progressions.
- Application of additive combinatorics methods.

## Abstract

Let H be a Krull monoid with finite class group G and suppose that every class contains a prime divisor. Then sets of lengths in H have a well-defined structure which just depends on the class group G. With methods from additive combinatorics we establish a characterization of those class groups G guaranteeing that all sets of lengths are (almost) arithmetical progressions.