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On Lattice Complements
Published online by Cambridge University Press: 18 May 2009
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Let (L, ≦) be a distributive lattice with first element 0 and last element 1. If a, b in L have complements, then these must be unique, and the De Morgan laws provide complements for a ∧ b and a ∨ b. We show that the converse statement holds under weaker conditions.
Theorem 1. If(L, ≦) is a modular lattice with 0 and 1 and if a, b in L are such that a ≦b and a ≨ b have (not necessarily unique) complements, then a andb have complements.
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- Copyright © Glasgow Mathematical Journal Trust 1965
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