Every abelian group is the class group of a simple Dedekind domain

Smertnig, Daniel

doi:10.1090/tran/6868

Every abelian group is the class group of a simple Dedekind domain
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by Daniel Smertnig PDF

Trans. Amer. Math. Soc. 369 (2017), 2477-2491 Request permission

Abstract:

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.

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