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

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.