No CrossRef data available.
Published online by Cambridge University Press: 20 November 2018
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.