Division rings with ranks
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- by Nadja Hempel and Daniel Palacín PDF
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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.References
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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
- MR Author ID: 1166052
- 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
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 803-817
- MSC (2010): Primary 03C45, 03C60, 12E15
- DOI: https://doi.org/10.1090/proc/13752
- MathSciNet review: 3731713