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.
Keywords
- MacNeille completion
- weakly dicomplemneted lattices
- Formal Concept Analysis
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Kwuida, L., Seselja, B., Tepavčević, A. (2007). On the MacNeille Completion of Weakly Dicomplemented Lattices. In: Kuznetsov, S.O., Schmidt, S. (eds) Formal Concept Analysis. ICFCA 2007. Lecture Notes in Computer Science(), vol 4390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70901-5_17
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DOI: https://doi.org/10.1007/978-3-540-70901-5_17
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