Complemented ordered sets

Ivan Chajda

Archivum Mathematicum (1992)

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

Abstract

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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.

How to cite

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Chajda, 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

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

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