Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice

• Autorzy: Ivan Chajda , Helmut Länger
• Języki publikacji: EN

Abstrakty

EN

Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.

Słowa kluczowe

EN

bounded lattice; antitone involution; complemented element

Kategorie tematyczne

• 06C15: Complemented lattices, orthocomplemented lattices and posets

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2008
• Tom: 28
• Numer: 2
• Strony: 251-259

Daty

wydano

2008

otrzymano

2008-06-13

poprawiono

2008-08-30

Twórcy

autor

Ivan Chajda

• Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 77900 Olomouc, Czech Republic

autor

Helmut Länger

• Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria

Bibliografia

• [1] G. Birkhoff, Lattice Theory, AMS, Providence, R. I., 1979.
• [2] I. Chajda and H. Länger, Bounded lattices with antitone involution the complemented elements of which form a sublattice, J. Algebra Discrete Structures 6 (2008), 13-22.
• [3] G. Grätzer, General Lattice Theory, Birkhäuser, Basel 1998.

Identyfikatory

DOI

10.7151/dmgaa.1147