Galois extensions of Boolean algebras
type: Item
instance of: scholarly article
title: Galois extensions of Boolean algebras
zbMATH Open document ID: 0939.06012
DOI: 10.1023/A:1006285832575
author: Žikica Perović
published in: Order
publication date: 2000-07-03T00:00:00Z
review text: Recall that automorphisms \(f,g\) are strongly distinct if for every nonzero element there is an \(s\) such that \(f(s)\cdot b\not=g(s)\cdot b\). \(B\) is Galois over \(C\) if \(\text{Fix}(G)=C\) for some subgroup \(G\) of strongly distinct members of \(\text{Aut}_CB\). The author shows that a finite extension \(B\) is Galois over \(C\) if and only if \(B\) is freely generated by a finite set over \(C\). This answers a question of the reviewer [see ``Automorphism groups'', in: J. D. Monk (ed.), Handbook of Boolean algebras (North-Holland, Amsterdam), 517-546 (1989; Zbl 0671.06001)].
Mathematics Subject Classification ID: 06E05
zbMATH DE Number: 1340443
zbMATH Keywords: Galois extensions
zbMATH Keywords: Boolean algebras
reviewed by: J. Donald Monk
MaRDI profile type: Publication
full work available at URL: a:1006285832575
OpenAlex ID: W2174524588
description: scientific article; zbMATH DE number 1340443