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.

中文翻译：

---

Krull monoid的表征，其长度的集合是（几乎）算术级数

假设$ H $是具有有限类组$ G $的Krull单面体，并假定每个类都包含一个素数除数。然后$ H $中的长度集具有定义明确的结构，该结构仅取决于类组$ G $。使用加法组合法的方法，我们建立了这些类组$ G $的表征，从而保证所有长度集都是（几乎）算术级数。