3
votes
0answers
79 views

Question about Wantzel's proof of the necessary condition for compass/straightedge constructibility

I'm trying to understand Wantzel's original proof of the necessary condition for constructibility with a straightedge and compass. It's expressed in terms of polynomials rather than field extensions. ...
2
votes
0answers
97 views

Finite/algebraic extensions of rational functions

I'm looking for results on the subject of finite/algebraic extensions of rational functions, but I only find papers who deal with algebraic geometry. I only know the basis of Galois theory. Could you ...
2
votes
2answers
406 views

finding a fixed field of a rational function field

let G be the subset of $\operatorname{aut}_{K} K(x)$ consisting of the three automorphisms $$ x \mapsto x $$ $$ x \mapsto 1/(1-x)$$ $$ x \mapsto (x-1)/x$$ then G is a subgroup of ...
0
votes
1answer
563 views

The field of rational functions in $n$ variables is a Galois extension of the field of symmetric rational polynomials in $n$ variables.

I've been doing a little bit of field theory for number fields but not much with function fields. The question originally asked says "For some field F, show that the field $F(u_1,\ldots, u_n)$ is a ...