Splittings of \(\widetilde{\mathbb Q} /\mathbb Q\)
type: Item
instance of: scholarly article
title: Splittings of \(\widetilde{\mathbb Q} /\mathbb Q\)
zbMATH Open document ID: 0954.12001
author: Aharon Razon
published in: Archiv der Mathematik
publication date: 2001-02-11T00:00:00Z
review text: Let \(K\) be a subfield of a field \(M.\) \(M\) is said to be PAC over \(K,\) if for every absolutely irreducible variety \(V\) of dimension \(r\geq 0\) and for each dominating separable rational map \(\varphi:V\to {\mathbb A}^r\) over \(M,\) there exists \(a\in V(M)\) such that \(\varphi (a)\in K^r.\) It is proved that if \(M\) is a PAC field over a subfield \(K\) and \(N\) is a separable algebraic extension of \(M\) then there exists a separable algebraic extension \(L\) of \(K,\) linearly disjoint from \(M,\) such that \(LM=N.\) Results are used from [\textit{M. Jarden} and \textit{A. Razon}, Isr. J. Math. 86, No.~1-3, 25--59 (1994; Zbl 0802.12007)].
Mathematics Subject Classification ID: 12E30
Mathematics Subject Classification ID: 12E25
Mathematics Subject Classification ID: 12F05
zbMATH DE Number: 1462954
zbMATH Keywords: absolutely irreducible variety
zbMATH Keywords: pseudo algebraically closed field
zbMATH Keywords: extension of a field
zbMATH Keywords: linearly disjoint separable extension
MaRDI profile type: Publication
full work available at URL: s000130050440
OpenAlex ID: W2030730889
DOI: 10.1007/S000130050440
description: scientific article; zbMATH DE number 1462954