Factorization in Krull monoids with infinite class group

Florian Kainrath

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The catenary degree of Krull monoids I

Alfred Geroldinger, David J. Grynkiewicz, Wolfgang A. Schmid (2011)

Journal de Théorie des Nombres de Bordeaux

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Let $H$ be a Krull monoid with finite class group $G$ such that every class contains a prime divisor (for example, a ring of integers in an algebraic number field or a holomorphy ring in an algebraic function field). The catenary degree $c (H)$ of $H$ is the smallest integer $N$ with the following property: for each $a \in H$ and each two factorizations $z, z^{'}$ of $a$ , there exist factorizations $z = z_{0}, ..., z_{k} = z^{'}$ of $a$ such that, for each $i \in [1, k]$ , $z_{i}$ arises from $z_{i - 1}$ by replacing at most $N$ atoms from $z_{i - 1}$ by at most $N$ new atoms. Under a very...