On Kneser extensions
type: Item
instance of: scholarly article
title: On Kneser extensions
zbMATH Open document ID: 0913.12003
author: P. Lam-Estrada
author: Fernando Barrera Mora
author: Gabriel D. Villa Salvador
published in: Journal of Algebra
publication date: 1998-11-29T00:00:00Z
review text: The concepts of \(G\)-Kneser field extension and \(G\)-Cogalois field extension were introduced by \textit{T. Albu} and \textit{F. Nicolae} [J. Number Theory 52, 299-318 (1995; Zbl 0838.12003)], in which they raised the following question: ``Let \(E/F\) be a finite separable field extension such that \(E=F(G)\), with \(F^*\leq G\leq E^*\), \(G/F^*\) a finite group, and such that the canonical maps between the subfields of the extension \(E/F\) and the subgroups of \(G/F^*\) are inverse isomorphisms of lattices. Does there exist another group \(\widetilde G\) with \(F^*\leq\widetilde G\leq E^*\) and \(G/F^*\) a finite group such that \(E/F\) is \(\widetilde G\)-Cogalois?'' A necessary and sufficient condition is given in the paper under review to answer the question positively. Examples in characteristic \(p>0\) and in characteristic 0 are given to show that the answer to the question above is in general negative.
Mathematics Subject Classification ID: 12F10
zbMATH DE Number: 1214121
zbMATH Keywords: Kneser extensions
zbMATH Keywords: radical extension
zbMATH Keywords: pure extension
zbMATH Keywords: \(G\)-Cogalois extension
zbMATH Keywords: separable field extension
reviewed by: Toma Albu
MaRDI profile type: Publication
full work available at URL: jabr.1997.7308
OpenAlex ID: W2056639333
cites work: Kneser field extensions with cogalois correspondence
cites work: On cogalois extensions
cites work: A Galois correspondence for radical extensions of fields
cites work: Lineare Abhängigkeit von Wurzeln
cites work: Q5565771
DOI: 10.1006/JABR.1997.7308
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description: scientific article; zbMATH DE number 1214121