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Division rings with ranks


Authors: Nadja Hempel and Daniel Palacín
Journal: Proc. Amer. Math. Soc. 146 (2018), 803-817
MSC (2010): Primary 03C45, 03C60, 12E15
DOI: https://doi.org/10.1090/proc/13752
Published electronically: September 7, 2017
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Abstract: Any superrosy division ring is shown to be centrally finite. Furthermore, division rings satisfying a generalized chain condition on definable subgroups are studied. In particular, a division ring of burden $ n$ has dimension at most $ n$ over its center, and any definable group of definable automorphisms of a field of burden $ n$ has size at most $ n$. Additionally, an alternative proof that division rings interpretable in o-minimal structures are algebraically closed, real closed or the quaternions over a real closed field is given.


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Additional Information

Nadja Hempel
Affiliation: Institut Camille Jordan, Université Lyon 1, 43 bd du 11 novembre 1918, 69622 Villeurbanne Cedex, France
Address at time of publication: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095-1555
Email: nadja@math.ucla.edu

Daniel Palacín
Affiliation: Mathematisches Institut, Universitat Münster, Einsteinstrasse 62, 48149 Münster, Germany
Address at time of publication: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram 9190401, Jerusalem, Israel
Email: daniel.palacin@mail.huji.ac.il

DOI: https://doi.org/10.1090/proc/13752
Received by editor(s): June 15, 2016
Received by editor(s) in revised form: February 24, 2017, and March 29, 2017
Published electronically: September 7, 2017
Additional Notes: The first author was supported by the project ValCoMo (ANR-13-BS01-0006)
The second author was supported by the projects SFB 878 and MTM2014-59178-P
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society

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