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

### Alfred Geroldinger

Universität Graz, Austria### Wolfgang Alexander Schmid

Université Paris 13, Villetaneuse, France

## 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 depends only 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.

## Cite this article

Alfred Geroldinger, Wolfgang Alexander Schmid, A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions. Rev. Mat. Iberoam. 37 (2021), no. 1, pp. 293–316

DOI 10.4171/RMI/1207