Distributive Sublattices of a Free Lattice

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Abstract
The purpose of this note is to characterize those distributive lattices that can be isomorphically embedded in free lattices. If it is known (cf. (2)) that in a free lattice every element is either additively or multiplicatively irreducible, and consequently every sublattice of a free lattice must also have this property. We therefore begin by studying the class of all those distributive lattices in which this condition is satisfied.

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