On subfields of rational function fields
type: Item
instance of: scholarly article
title: On subfields of rational function fields
zbMATH Open document ID: 0546.12013
DOI: 10.1007/BF01772932
author: Jack Ohm
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: Let \(k\subset K\) and \(k\subset L\) be field extensions. Suppose that \(L\) is contained in a purely transcendental extension of \(K\). Then \(L\) is \(k\)-isomorphic to a subfield of \(K\), provided the degree of transcendency of \(L| k\) satisfies: \(dt L| k\leq dt K| k.\) This statement constitutes as useful lemma in certain investigations of unirational fields. Until now, however, it was proved in the literature for infinite base field \(k\) only. The proof presented here is valid also for finite base field.
reviewed by: Peter Roquette
Mathematics Subject Classification ID: 12F20
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 14G05
zbMATH DE Number: 3869473
zbMATH Keywords: purely transcendental extension
zbMATH Keywords: degree of transcendency
zbMATH Keywords: unirational fields
MaRDI profile type: Publication
cites work: Ruled Function Fields
cites work: A Theorem on Valuation Rings and its Applications
cites work: Isomorphisms of generic splitting fields of simple algebras.
cites work: Q4771357
cites work: Q5732721
full work available at URL: https://doi.org/10.1007/bf01772932
OpenAlex ID: W1985868940
description: scientific article; zbMATH DE number 3869473