On a problem of Kaplansky II: Every finitely generated Abelian group is the restricted Grothendieck group of a local, Noetherian, Krull domain

Abstract

For every finitely generated Abelian group G, we construct a local, Noetherian, Krull-domain R, for which the restricted Grothendieck group G ̃ 0(R) is isomorphic to G. Furthermore, G ̃ 0(R) is naturally isomorphic to the divisor class group C( R) of R.