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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

2 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	1291-1293
Nombre de pages	3
journal	Turkish Journal of Mathematics
Volume	46
Numéro de publication	4
Les DOIs	https://doi.org/10.3906/mat-2110-11
état	Publié - 1 janv. 2022

Accès au document

10.3906/mat-2110-11

Contient cette citation

@article{4cef1d08010346cc8f6bfeed71fac542,

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.",

keywords = "L{\"u}roth{\textquoteright}s theorem, One transcendence degree, Simple extension",

author = "Fran{\c c}ois Ollivier and Brahim Sadik",

note = "Publisher Copyright: {\textcopyright} This work is licensed under a Creative Commons Attribution 4.0 International License.",

year = "2022",

month = jan,

day = "1",

doi = "10.3906/mat-2110-11",

language = "English",

volume = "46",

pages = "1291--1293",

journal = "Turkish Journal of Mathematics",

issn = "1300-0098",

publisher = "TUBITAK",

number = "4",

}

TY - JOUR

T1 - A simple and constructive proof to a generalization of Lüroth’s theorem

AU - Ollivier, François

AU - Sadik, Brahim

N1 - Publisher Copyright: © This work is licensed under a Creative Commons Attribution 4.0 International License.

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

KW - One transcendence degree

KW - Simple extension

U2 - 10.3906/mat-2110-11

DO - 10.3906/mat-2110-11

M3 - Article

AN - SCOPUS:85131421011

SN - 1300-0098

VL - 46

SP - 1291

EP - 1293

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 4

ER -

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

Résumé

Accès au document

Empreinte digitale

Contient cette citation