  A classical result of Claborn states that every abelian group is the class
group of a commutative Dedekind domain. Among noncommutative Dedekind prime
rings, apart from PI rings, the simple Dedekind domains form a second important
class. We show that every abelian group is the class group of a noncommutative
simple Dedekind domain. This solves an open problem stated by Levy and Robson
in their recent monograph on hereditary Noetherian prime rings.
