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Discussiones Mathematicae General Algebra and Applications 20(2) (2000) 207-217
DOI: https://doi.org/10.7151/dmgaa.1018

RELATIVELY COMPLEMENTED ORDERED SETS

Ivan Chajda and Zuzana Morávková

Department of Algebra and Geometry, Palacký University of Olomouc
Tomkova 40, 779 00 Olomouc, Czech Republic
e-mail: chajda@risc.upol.cz

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.

Key words and phrases: modular ordered set, complemented, relatively complemented ordered set, atom.

1991 Mathematics Subject Classification: 06A99.

References

[1]	I. Chajda, Complemented ordered sets, Arch. Math. (Brno) 28 (1992), 25-34.
[2]	I. Chajda and J. Rach23 unek, Forbidden configurations for distributive andmodular ordered sets, Order 5 (1989), 407-423.
[3]	R. Halas, Pseudocomplemented ordered sets, Arch. Math. (Brno) 29 (1993), 153-160.
[4]	J. Niederle, Boolean and distributive ordered sets, Order 12 (1995), 189-210.
[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.
[6]	V.N. Salij, Lettices with Unique Complementations (Russian), Nauka, Moskva 1984.

Received 21 September 1998
Revised 7 June 1999