Elliptic Dedekind Domains Revisited

Details Elliptic Dedekind Domains Revisited Elliptic Dedekind Domains Revisited

2008-05-08

arxiv.org/abs/0805.1082v1

Mathematics

Commutative Algebra

9 pages

Scientific paper

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 separable quadratic field
extension. In particular, this yields new and -- we feel -- simpler proofs of
theorems of L. Claborn and C.R. Leedham-Green.

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