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Characterization of extremal valued fields


Authors: Salih Azgin, Franz-Viktor Kuhlmann and Florian Pop
Journal: Proc. Amer. Math. Soc. 140 (2012), 1535-1547
MSC (2010): Primary 12J10; Secondary 12E30
DOI: https://doi.org/10.1090/S0002-9939-2011-11020-7
Published electronically: September 21, 2011
MathSciNet review: 2869138
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Abstract: We characterize those valued fields for which the image of the valuation ring under every polynomial in several variables contains an element of maximal value or zero.


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Additional Information

Salih Azgin
Affiliation: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, L8S 4K1 Ontario, Canada
Address at time of publication: Middle Eastern Technical University, Northern Cyprus Campus, Kalkanlı, Güzelyurt, KKTC, Mersin 10, Turkey
Email: sazgin@math.mcmaster.ca, sazgin@metu.edu.tr

Franz-Viktor Kuhlmann
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6
Email: fvk@math.usask.ca

Florian Pop
Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395
Email: pop@math.upenn.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-11020-7
Received by editor(s): July 1, 2009
Received by editor(s) in revised form: September 22, 2009, April 11, 2010, and January 20, 2011
Published electronically: September 21, 2011
Additional Notes: The second author was partially supported by a Canadian NSERC grant and by a sabbatical grant of the University of Saskatchewan.
The third author was supported by the John Templeton Foundation grant ID 13394. \indent A major part of this research was done while the authors were attending the o-minimality program at the Fields Institute, January–June 2009. The authors would like to thank the Fields Institute for its support and hospitality.
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.