Some remarks on subfields of algebraic number fields
type: Item
instance of: scholarly article
title: Some remarks on subfields of algebraic number fields
zbMATH Open document ID: 0866.12003
DOI: 10.1007/BF02341497
author: H. Markšaitis
published in: Lithuanian Mathematical Journal
publication date: 1996-10-29T00:00:00Z
review text: In this note it is proved that if \(k\) is an algebraic number field, for every positive integer \(n\), there exist infinitely many field extensions of \(k\) of degree \(n\) having no proper subfields over \(k\). This result is deduced from the existence of infinitely many polynomials of degree \(n\) over \(k\) with Galois group \(S_n\) and of no proper subgroups between \(S_n\) and \(S_{n-1}\).
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 11R32
zbMATH DE Number: 939524
zbMATH Keywords: subfields
zbMATH Keywords: Galois theory
zbMATH Keywords: algebraic number field
zbMATH Keywords: Galois group
reviewed by: Nuria Vila
MaRDI profile type: Publication
cites work: Q5830710
full work available at URL: https://doi.org/10.1007/bf02341497
OpenAlex ID: W2022108843
description: scientific article; zbMATH DE number 939524