Distributivity and the normal completion of Boolean algebras

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Distributivity of the Normal Completion, and Its Priestley Representation

The normal, or Dedekind-MacNeille, completion δ(L) of a distributive lattice L need not be distributive. However, δ(L) does contain a largest distributive sublattice β(L) containing L, and δ(L) is distributive if and only if β(L) is complete if and only if δ(L) = β(L). In light of these facts, it may come as a surprise to learn that β(L) was developed (in [1]) for reasons having nothing to do w...

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ژورنال

عنوان ژورنال: Pacific Journal of Mathematics

سال: 1958

ISSN: 0030-8730,0030-8730

DOI: 10.2140/pjm.1958.8.133