Generalized Sets of Lengths Original Research Article

LetRbe a Dedekind domain and image(R) the set of irreducible elements ofR. In this paper, we study the sets imageR(n) = {m there exists α1,…,αn, β1,…,βm set membership, variant image(R) such that α1,…,αn = β1,…,βm}, wherenis a positive integer. We show, in constrast to indications in some earlier work, that the sets imageR(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]].