On the MacNeille completion of weakly dicomplemented lattices

  • Authors:

  • Léonard Kwuida;Branimir Seselja;Andreja Tepavčevic

  • Affiliations:

  • Universität Bern, Mathematisches Institut, Bern;University of Novi Sad, Department of Mathematics and Informatics, Novi Sad;University of Novi Sad, Department of Mathematics and Informatics, Novi Sad

  • Venue:
  • ICFCA'07 Proceedings of the 5th international conference on Formal concept analysis
  • Year:
  • 2007

Quantified Score

Hi-index 0.02

Visualization

Abstract

The MacNeille completion of a poset (P, ≤) is the smallest (up to isomorphism) complete poset containing (P, ≤) that preserves existing joins and existing meets. It is wellknown that the MacNeille completion of a Boolean algebra is a Boolean algebra. It is also wellknown that the MacNeille completion of a distributive lattice is not always a distributive lattice (see [Fu44]). The MacNeille completion even seems to destroy many properties of the initial lattice (see [Ha93]). Weakly dicomplemented lattices are bounded lattices equipped with two unary operations satisfying the equations (1) to (3') of Theorem 3. They generalise Boolean algebras (see [Kw04]). The main result of this contribution states that under chain conditions the MacNeille completion of a weakly dicomplemented lattice is a weakly dicomplemented lattice. The needed definitions are given in subsections 1.2 and 1.3. 2000 Mathematics Subject Classification: 06B23.