On the reconstruction of boolean algebras from their automorphism groups

Matatyahu Rubin

doi:10.1007/BF02021132

On the reconstruction of boolean algebras from their automorphism groups

Matatyahu Rubin

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3 Scopus citations

Abstract

A Boolean algebra B is called faithful, if for every direct summand B₁ of B: if B₁ is rigid, (that is, it does not have any automorphisms other than the identity), then there is B₂ such that B≅B₁×B₁×B₁×B₂. Let B be a complete Boolean algebra, then B can be uniquely represented as B≅B^R×B^D×B^D×B^F, where B^R, B^D, B^F are pairwise totally different, (that is, no two of them have non-zero isomorphic direct summands), B^R, B^D are rigid and B^F is faithful. Aut(B) denotes the automorphism group of B.

Original language	English
Pages (from-to)	125-146
Number of pages	22
Journal	Archiv für Mathematische Logik und Grundlagenforschung
Volume	20
Issue number	3-4
DOIs	https://doi.org/10.1007/BF02021132
State	Published - 1 Sep 1980
Externally published	Yes

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Logic

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10.1007/BF02021132

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On the reconstruction of boolean algebras from their automorphism groups

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