Geodesic
Relatively complemented ordered sets
Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 2, pp. 207-217

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We investigate conditions for the existence of relative complements in ordered sets. For relatively complemented ordered sets with 0 we show that each element b ≠ 0 is the least one of the set of all upper bounds of all atoms contained in b.
Keywords: modular ordered set, complemented, relatively complemented ordered set, atom 
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Chajda, Ivan; Morávková, Zuzana. Relatively complemented ordered sets. Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 2, pp. 207-217. http://geodesic.mathdoc.fr/item/DMGAA_2000_20_2_a5/