Relatively complemented ordered sets

• Autorzy: Ivan Chajda , Zuzana Morávková
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

modular ordered set; complemented; relatively complemented ordered set; atom

Kategorie tematyczne

• 06A99: None of the above, but in this section

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2000
• Tom: 20
• Numer: 2
• Strony: 207-217

Daty

wydano

2000

otrzymano

1998-08-21

poprawiono

1999-06-07

Twórcy

autor

Ivan Chajda

• Department of Algebra and Geometry, Palacký University of Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic

autor

Zuzana Morávková

• Department of Algebra and Geometry, Palacký University of Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgaa.1018