A simple and constructive proof to a generalization of Lüroth's theorem

Authors: FRANCOIS OLLIVIER, BRAHIM SADIK

Abstract: A generalization of Lüroth'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: Lüroth's theorem, one transcendence degree, simple extension

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