On the reconstruction of boolean algebras from their automorphism groups

  • Matatyahu Rubin
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Abstract

A Boolean algebraB is called faithful, if for every direct summandB1 ofB: ifB1 is rigid, (that is, it does not have any automorphisms other than the identity), then there isB2 such thatB≅B1×B1×B1×B2. LetB be a complete Boolean algebra, thenB can be uniquely represented asB≅BR×BD×BD×BF, whereBR,BD,BF are pairwise totally different, (that is, no two of them have non-zero isomorphic direct summands),BR,BD are rigid andBF is faithful. Aut(B) denotes the automorphism group ofB.

Keywords

Mathematical Logic Automorphism Group Boolean Algebra Direct Summand Complete Boolean Algebra 
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Copyright information

© Verlag W. Kohlhammer 1980

Authors and Affiliations

  • Matatyahu Rubin
    • 1
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA

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