Composites of algebraically closed fields
type: Item
instance of: scholarly article
title: Composites of algebraically closed fields
zbMATH Open document ID: 0705.12005
DOI: 10.1016/0021-8693(90)90107-Y
author: Daniel B. Shapiro
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: Let \(k\) be an algebraically closed field, and suppose that \(K\) is a composite of extension fields \(K_i\) which are linearly disjoint over \(k\). The author proves that if \(k\subseteq L\subseteq K\), where \(L\) is a field with \(L^q=L\) for some prime \(q\) not equal to the characteristic of the fields, then \(L\subseteq K_i\) for some \(i\). The proof is obtained from the study of composites of two linearly disjoint, algebraically closed extensions of \(k\); and some interesting properties of such a composite are demonstrated. In particular, purity of an element \(z\) of a composite \(K_1K_2\), i.e. when \(z=z_1z_2\) for \(z_ i\in K_i\) is investigated.
reviewed by: H. F. Kreimer
Mathematics Subject Classification ID: 12F20
Mathematics Subject Classification ID: 12L12
zbMATH DE Number: 4156595
zbMATH Keywords: composites of fields
zbMATH Keywords: free composite
zbMATH Keywords: linearly disjoint, algebraically closed extensions
MaRDI profile type: Publication
cites work: Q5531597
cites work: A Borel reductibility theory for classes of countable structures
cites work: Q5603302
cites work: Q5659683
cites work: Q5588717
description: scientific article; zbMATH DE number 4156595