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Images of Additive Polynomials in 𝔽q((t)) Have the Optimal Approximation Property

Published online by Cambridge University Press:  20 November 2018

Lou van den Dries  and
Franz-Viktor Kuhlmann
Lou van den Dries
Affiliation:
Department of Mathematics, University of Illinois at Urbana, 273 Altgeld Hall, 1409 West Green Street, Urbana, IL 61801, USA, email: vddries@math.uiuc.edu
Franz-Viktor Kuhlmann
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, S7N 5E6, email: fvk@math.usask.ca
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Abstract

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We show that the set of values of an additive polynomial in several variables with arguments in a formal Laurent series field over a finite field has the optimal approximation property: every element in the field has a (not necessarily unique) closest approximation in this set of values. The approximation is with respect to the canonical valuation on the field. This property is elementary in the language of valued rings.

Keywords

12J1012L1203C60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 71 - 79
Copyright
Copyright © Canadian Mathematical Society 2002

References

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[L] Lang, S., Algebra. Addison-Wesley, New York, 1965.Google Scholar