DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

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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


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