Relatively complemented ordered sets

Ivan Chajda; Zuzana Morávková

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 2, page 207-217
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Ivan Chajda, and Zuzana Morávková. "Relatively complemented ordered sets." Discussiones Mathematicae - General Algebra and Applications 20.2 (2000): 207-217. <http://eudml.org/doc/287670>.

@article{IvanChajda2000,
abstract = {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.},
author = {Ivan Chajda, Zuzana Morávková},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {modular ordered set; complemented; relatively complemented ordered set; atom},
language = {eng},
number = {2},
pages = {207-217},
title = {Relatively complemented ordered sets},
url = {http://eudml.org/doc/287670},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Ivan Chajda
AU - Zuzana Morávková
TI - Relatively complemented ordered sets
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 2
SP - 207
EP - 217
AB - 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.
LA - eng
KW - modular ordered set; complemented; relatively complemented ordered set; atom
UR - http://eudml.org/doc/287670
ER -

References

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  1. [1] I. Chajda, Complemented ordered sets, Arch. Math. (Brno) 28 (1992), 25-34. Zbl0785.06002
  2. [2] I. Chajda and J. Rach23 unek, Forbidden configurations for distributive andmodular ordered sets, Order 5 (1989), 407-423. 
  3. [3] R. Halas, Pseudocomplemented ordered sets, Arch. Math. (Brno) 29 (1993), 153-160. Zbl0801.06007
  4. [4] J. Niederle, Boolean and distributive ordered sets, Order 12 (1995), 189-210. Zbl0838.06004
  5. [5] J. Rach23 unek and J. Larmerová, Translations of modular and distributive ordered sets, Acta Univ. Palacký Olomouc, Fac. Rerum Nat., Math., 31 (1988), 13-23. Zbl0693.06003
  6. [6] V.N. Salij, Lettices with Unique Complementations (Russian), Nauka, Moskva 1984. 

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