Geodesic
Complemented ordered sets
Archivum mathematicum, Tome 28 (1992) no. 1-2, pp. 25-34 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 
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     author = {Chajda, Ivan},
     title = {Complemented ordered sets},
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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/

[1] Birkhoff G.: Lattice Theory. Amer. Math. Soc. Colloq. Publ. 25 (1967), N.Y., (3-rd edition). | MR | Zbl

[2] Chajda I., Rachůnek J.: Forbidden configurations for distributive and modular ordered sets. Order 5 (1989), 407 – 423. | MR

[3] Grätzer G.: General Lattice Theory. Basel, Stuttgart, 1978. | MR

[4] Larmerová J., Rachůnek J.: Translations of distributive and modular ordered sets. Acta Univ. Palack. (to appear), Olomouc.

[5] Pierce G.S.: On the algebra of logic. Amer. J. Math. (1980), 15 – 57.

[6] Rachůnek J.: Translations des ensembles ordonés. Math. Slovaca 31 (1981), 337 – 340. | MR

[7] Salij V.N.: Uniquely complemented lattices. Nauka, Moskva, 1984, (in Russian).