From: Robin Chapman <rjchapman@mailandnews.co.uk>
Subject: RE: Algebraically Closed Field Extensions
Date: Sat, 16 Jun 2001 14:14:10 -0400
Newsgroups: sci.math
Summary: Fields of finite index in their algebraic closure

>===== Original Message From AndrEs Eduardo Caicedo 
<acaicedo@math.berkeley.edu> =====
>It is relatively well known that if K is a field of characteristic 0 and
>L is an algebraic extension of K such that
> 1<[L:K]<infinity
>and L is algebraically closed, then
> [L:K]=2,
> L=K(square root of -1), and
> K is a real-closed field.
>
>Is it possible to have char K different from 0 and 1<[L:K]<infinity,
>with L algebraically closed?

No. See e.g., Lang's Algebra.

------------------------------------------------------------
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"His mind has been corrupted by colours, sounds and shapes."
 The League of Gentlemen