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Going-Down Results for Ci-Fields

Published online by Cambridge University Press:  20 November 2018

Anthony J. Bevelacqua  and
Mark J. Motley
Anthony J. Bevelacqua
Affiliation:
Department of Mathematics, University of North Dakota, Grand Forks, North Dakota 58202, USA email: anthony_bevelacqua@und.nodak.edu
Mark J. Motley
Affiliation:
Department of Mathematics, Pikeville College, Pikeville, Kentucky 41501, USA email: mmotley@pc.edu
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Abstract

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We search for theorems that, given a ${{C}_{i}}$-field $K$ and a subfield $k$ of $K$, allow us to conclude that $k$ is a ${{C}_{j}}$ -field for some $j$. We give appropriate theorems in the case $\text{case }K=k\left( t \right)$ and $K=k\left( \left( t \right) \right)$. We then consider the more difficult case where $K/k$ is an algebraic extension. Here we are able to prove some results, and make conjectures. We also point out the connection between these questions and Lang's conjecture on nonreal function fields over a real closed field.

Keywords

12F14GCi-fieldsLang's Conjecture
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 1 , 01 March 2006 , pp. 11 - 20
Copyright
Copyright © Canadian Mathematical Society 2006

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