  Let $H$ be a Krull monoid with class group $G$ and suppose that each class
contains a prime divisor. Then every element $a \in H$ has a factorization into
irreducible elements, and the set $\mathsf L (a)$ of all possible factorization
lengths is the set of lengths of $a$. We consider the system $\mathcal L (H) =
\{ \mathsf L (a) \mid a \in H \}$ of all sets of lengths, and we characterize
(in terms of the class group $G$) when $\mathcal L (H)$ is additively closed
under set addition.

Commutative Algebra;Combinatorics