Galois extensions of Boolean algebras
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)].
scientific article; zbMATH DE number 1340443