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.
@article{107433,
author = {Ivan Chajda},
title = {Complemented ordered sets},
journal = {Archivum Mathematicum},
volume = {028},
year = {1992},
pages = {25-34},
zbl = {0785.06002},
mrnumber = {1201863},
language = {en},
url = {http://dml.mathdoc.fr/item/107433}
}
Chajda, Ivan. Complemented ordered sets. Archivum Mathematicum, Tome 028 (1992) pp. 25-34. http://gdmltest.u-ga.fr/item/107433/
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