English

A simple and constructive proof to a generalization of L\"uroth's theorem

Commutative Algebra 2022-09-23 v2 Symbolic Computation Number Theory

Abstract

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.

Keywords

Cite

@article{arxiv.2201.11733,
  title  = {A simple and constructive proof to a generalization of L\"uroth's theorem},
  author = {François Ollivier and Brahim Sadik},
  journal= {arXiv preprint arXiv:2201.11733},
  year   = {2022}
}

Comments

5 pages

R2 v1 2026-06-24T09:06:04.347Z