On the arithmetic of Krull monoids with finite Davenport constant

Let H be a Krull monoid with class group G, GP⊂G the set of classes containing prime divisors and D(GP) the Davenport constant of GP. We show that the finiteness of the Davenport constant implies the Structure Theorem for Sets of Lengths. More precisely, if D(GP)<∞, then there exists a constant M—for which we derive an explicit upper bound in terms of D(GP)—such that the set of lengths of every element a∈H is an almost arithmetical multiprogression with bound M.