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 . We can choose 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.
Cite this article
Pete L. Clark, Elliptic Dedekind Domains Revisited. Enseign. Math. 55 (2009), no. 3/4, pp. 213–225DOI 10.4171/LEM/55-3-1