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Keywords:
modular ordered set; distributive ordered set; complemented ordered set; projective plane
modular ordered set; distributive ordered set; complemented ordered set; projective plane
Summary:
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.
References:
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[7] Salij V.N.: Uniquely complemented lattices. Nauka, Moskva, 1984, (in Russian).
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