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ArticleOriginal scientific text

Title

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

Authors 1, 2

Affiliations

  1. Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 77900 Olomouc, Czech Republic
  2. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria

Abstract

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.

Keywords

ENG
bounded lattice, antitone involution, complemented element

Bibliography

  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.
Discussiones Mathematicae - General Algebra and Applications
2008/28/2
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Pages:
251-259
Main language of publication
English
Received
2008-06-13
Accepted
2008-08-30
Published
2008

DOI: 10.7151/dmgaa.1147

Exact and natural sciences