Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transcendental Galois Theory and Noether's Problem   In 1918, Noether published a paper where she studied such a problem, now
called Noether's problem on rationality: Let $L=K\left( t_{1},t_{2},\cdots
,t_{n}\right) $ be a purely transcendental extension over a field $K$ and $G$ a
finite subgroup acting transitively on $t_{1},t_{2},\cdots ,t_{n}$ in an
evident manner. Is it true that the invariant subfield $L^{G}$ of $L$ under $%
G$ is still purely transcendental over $K$? The problem has been open in
general except for minor particular cases. In this paper we will attempt to
understand a general theory for Noether's problem on rationality by
transcendental Galois theory. Then new particular cases will be obtained. We
will also give a generalization for the remarkable counter-example given by
Swan in 1969.

17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
19
The categories of this paper are: eess
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat