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Boolean algebra embeddings

  1. Dec 9, 2007 #1

    quasar987

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    According to my notes, the definition of an embedding from a boolean algebra B in a boolean algebra B' is an injective map f:B-->B' such that for all x,y in B, f(sup{x,y}) = sup'{f(x),f(y)} and f(Cx)=C'(f(x)), where sup is the supremum in B and sup' is the complement in B', and where C is the complement in B and C' the complement in B'.

    But I read on wiki that generally, an embedding is supposed to be a monomorphism. Aren't we missing the condition f(inf{x,y}) = inf'{f(x),f(y)}???
     
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  3. Dec 9, 2007 #2

    Hurkyl

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    Doesn't it follow from the other ones?
     
  4. Dec 9, 2007 #3

    quasar987

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    Right, because of the de Morgan laws !
     
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