Name
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. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/978-3-540-70901-5_17 | ICFCA |
Keywords | Field | DocType |
distributive lattice,weakly dicomplemented lattice,boolean algebra,complete poset,macneille completion,contribution state,mathematics subject classification,bounded lattice,chain condition,initial lattice,satisfiability,formal concept analysis | Discrete mathematics,Combinatorics,Distributive lattice,Unary operation,Lattice (order),Dedekind–MacNeille completion,Isomorphism,Boolean algebra,Complete Boolean algebra,Mathematics,Partially ordered set | Conference |
Volume | ISSN | Citations |
4390 | 0302-9743 | 1 |
PageRank | References | Authors |
0.43 | 2 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Léonard Kwuida | 1 | 55 | 16.25 |
| Branimir Seselja | 2 | 63 | 10.90 |
| Andreja Tepavčevic | 3 | 39 | 8.83 |