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


Author: Daniel Smertnig
Journal: Trans. Amer. Math. Soc. 369 (2017), 2477-2491
MSC (2010): Primary 16E60; Secondary 16N60, 16P40, 19A49
DOI: https://doi.org/10.1090/tran/6868
Published electronically: July 20, 2016
MathSciNet review: 3592518
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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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Additional Information

Daniel Smertnig
Affiliation: Institute for Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstraße 36, 8010 Graz, Austria
Email: daniel.smertnig@uni-graz.at

DOI: https://doi.org/10.1090/tran/6868
Keywords: Simple Dedekind prime rings, ideal class groups
Received by editor(s): April 8, 2015
Published electronically: July 20, 2016
Additional Notes: The author was supported by the Austrian Science Fund (FWF) project P26036-N26.
Article copyright: © Copyright 2016 American Mathematical Society