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On uniquely complemented posets. (English) Zbl 1091.06002
The authors extend some classical results of uniquely complemented lattices to uniquely complemented posets with $$0$$ and $$1$$. They prove that a uniquely complemented join-semilattice having the general disjointness property is Boolean. They extend the Birkhoff-von Neumann theorem to larger classes of lattices, such as the class of modular lattices with the general disjointness property.

##### MSC:
 06A06 Partial orders, general 06A12 Semilattices 06C05 Modular lattices, Desarguesian lattices 06C15 Complemented lattices, orthocomplemented lattices and posets 06C20 Complemented modular lattices, continuous geometries 06D15 Pseudocomplemented lattices
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