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

François Ollivier; Brahim Sadik

doi:10.3906/mat-2110-11

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

François Ollivier
, Brahim Sadik

Cadi Ayyad University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1291-1293
Number of pages	3
Journal	Turkish Journal of Mathematics
Volume	46
Issue number	4
DOIs	https://doi.org/10.3906/mat-2110-11
Publication status	Published - 1 Jan 2022

Keywords

Lüroth’s theorem
One transcendence degree
Simple extension

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10.3906/mat-2110-11

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title = "A simple and constructive proof to a generalization of L{\"u}roth{\textquoteright}s theorem",

abstract = "generalization of L{\"u}roth{\textquoteright}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.",

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AU - Sadik, Brahim

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PY - 2022/1/1

Y1 - 2022/1/1

N2 - 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.

AB - 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.

KW - Lüroth’s theorem

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KW - Simple extension

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DO - 10.3906/mat-2110-11

M3 - Article

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JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 4

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

Abstract

Keywords

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