The Monotone Catenary Degree of Krull Monoids

Let H be a Krull monoid with finite class group G such that every class contains a prime divisor. The monotone catenary degree c (mon) (H) of H is the smallest integer m with the following property: for each and each two factorizations z, z' of a with length |z| a parts per thousand currency sign |z'|, there exist factorizations z = z (0), ... ,z (k) = z' of a with increasing lengths-that is, |z (0)| a parts per thousand currency sign ... a parts per thousand currency sign |z (k) |-such that, for each , z (i) arises from z (i-1) by replacing at most m atoms from z (i-1) by at most m new atoms. Up to now there was only an abstract finiteness result for c (mon) (H), but the present paper offers the first explicit upper and lower bounds for c (mon) (H) in terms of the group invariants of G.