Generalized Sets of Lengths

LetRbe a Dedekind domain and (R) the set of irreducible elements ofR. In this paper, we study the sets R(n) = {m α1,…,αn, β1,…,βm (R) such that α1,…,αn = β1,…,βm}, wherenis a positive integer. We show, in constrast to indications in some earlier work, that the sets R(n) are not completely determined by the Davenport constant of the class group ofR. We offer some specific constructions for Dedekind domains with small class groups, and show how these sets are generalizations of the sets studied earlier by Geroldinger [[9], [10]].