I'm looking for an explicit example of a uniquely complemented lattice that is non-modular, since neither of the two non-modular lattices described here at wikipedia have this property.
Thanks.
2026-04-01 13:49:02.1775051342
Uniquely complemented lattice that is non-modular
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We know that uniquely complemented lattices that are non-modular exist. This follows from the celebrated result by Dilworth (pdf). As far as I know, we do not know how to exhibit a concrete example, all the known constructions use some sort of complicated colimit. See the Graetzers paper in Notices (pdf) for a general overview of results concerning unique complementation and much more.