# Complemented ordered sets

Archivum Mathematicum (1992)

- Volume: 028, Issue: 1-2, page 25-34
- ISSN: 0044-8753

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topChajda, Ivan. "Complemented ordered sets." Archivum Mathematicum 028.1-2 (1992): 25-34. <http://eudml.org/doc/247351>.

@article{Chajda1992,

abstract = {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.},

author = {Chajda, Ivan},

journal = {Archivum Mathematicum},

keywords = {modular ordered set; distributive ordered set; complemented ordered set; projective plane; complemented ordered sets; complementarity; modularity; distributivity; projective planes},

language = {eng},

number = {1-2},

pages = {25-34},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Complemented ordered sets},

url = {http://eudml.org/doc/247351},

volume = {028},

year = {1992},

}

TY - JOUR

AU - Chajda, Ivan

TI - Complemented ordered sets

JO - Archivum Mathematicum

PY - 1992

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 028

IS - 1-2

SP - 25

EP - 34

AB - 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.

LA - eng

KW - modular ordered set; distributive ordered set; complemented ordered set; projective plane; complemented ordered sets; complementarity; modularity; distributivity; projective planes

UR - http://eudml.org/doc/247351

ER -

## References

top- Lattice Theory, Amer. Math. Soc. Colloq. Publ. 25 (1967), N.Y., (3-rd edition). (1967) Zbl0153.02501MR0227053
- Forbidden configurations for distributive and modular ordered sets, Order 5 (1989), 407 – 423. (1989) MR1010389
- General Lattice Theory, Basel, Stuttgart, 1978. (1978) MR0509213
- Translations of distributive and modular ordered sets, Acta Univ. Palack. (to appear), Olomouc. (to appear)
- On the algebra of logic, Amer. J. Math. (1980), 15 – 57. (1980)
- Translations des ensembles ordonés, Math. Slovaca 31 (1981), 337 – 340. (1981) MR0637961
- Uniquely complemented lattices, Nauka, Moskva, 1984, (in Russian). (1984)

## Citations in EuDML Documents

top- Ivan Chajda, Zuzana Morávková, Relatively complemented ordered sets
- Radomír Halaš, Concept lattices of quasiordered sets
- Petr Emanovský, Convex isomorphic ordered sets
- Radomír Halaš, A characterization of finite Stone pseudocomplemented ordered sets
- Ivan Chajda, Radomír Halaš, Characterizing triplets for modular pseudocomplemented ordered sets
- Vinayak Joshi, Nilesh Mundlik, Prime ideals in 0-distributive posets

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