Elliptic Dedekind Domains Revisited

Abstract

We give an affirmative answer to a 1976 question of M. Rosen: every abelian group is isomorphic to the class group of an elliptic Dedekind domain R . We can choose R to be the integral closure of a PID in a quadratic field extension. In particular, this yields new and – we feel – simpler proofs of theorems of L. Claborn and C.R. Leedham-Green.