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. © 2008 Elsevier Inc. All rights reserved.

Publication Title

Journal of Algebra