Geodesic
Complemented ordered sets
Archivum mathematicum, Tome 28 (1992) no. 1-2, pp. 25-34

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MR Zbl
We introduce the concept of complementary elements in ordered sets. If an ordered set $S$ is a lattice, this concept coincides with that for lattices. The connections between distributivity and the uniqueness of complements are shown and it is also shown that modular complemented ordered sets represents “geometries” which are more general than projective planes.
We introduce the concept of complementary elements in ordered sets. If an ordered set $S$ is a lattice, this concept coincides with that for lattices. The connections between distributivity and the uniqueness of complements are shown and it is also shown that modular complemented ordered sets represents “geometries” which are more general than projective planes.
Classification : 06A06
Keywords: modular ordered set; distributive ordered set; complemented ordered set; projective plane 
Chajda, Ivan. Complemented ordered sets. Archivum mathematicum, Tome 28 (1992) no. 1-2, pp. 25-34. http://geodesic.mathdoc.fr/item/ARM_1992_28_1-2_a4/
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