Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple and constructive proof to a generalization of L\"uroth's
  theorem   A generalization of L{\"u}roth's theorem expresses that every transcendence
degree 1 subfield of the rational function field is a simple extension. In this
note we show that a classical proof of this theorem also holds to prove this
generalization.

20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci