Complemented Lattices


Let L be a complemented lattice. That is a lattice with
a top or max element 1 and a bottom or min element 0 and
for all x in L, some y in L with
xy = inf x,y = 0, x + y = sup x,y = 1

x and y with that property are call complements.

If L is a distributive lattice, then each element has
exactly one complement. Is the converse correct,
that if L is complemented lattice for which every element
has a unique complement, then L is distributive? How does
one go about proving that?

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