Name
Abstract | ||
|---|---|---|
Let J be a fixed partially ordered set (poset). Among all posets in which J is join-dense and consists of all completely join-irreducible elements, there is an up to isomorphism unique greatest one, the Alexandroff completion L. Moreover, the class of all such posets has a canonical set of representatives, C0L, consisting of those sets between J and L which intersect each of the intervals Ij=[j?,j?] (j?J), where j? and j? denote the greatest element of L less than, respectively, not greater than j. The complete lattices in C0L form a closure system C8L, consisting of all Dedekind–MacNeille completions of posets in C0L. We describe explicitly those L for which C0L, respectively, C8L is a (complete atomic) Boolean lattice, and similarly, those for which C8L is distributive (or modular). Analogous results are obtained for C?L, the closure system of all posets in C0L that are closed under meets of less than ? elements (where ? is any cardinal number). |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1023/A:1024438130716 | Order |
Keywords | DocType | Volume |
complete lattice,completion,(completely) irreducible,join-dense,poset | Journal | 20 |
Issue | ISSN | Citations |
1 | 1572-9273 | 2 |
PageRank | References | Authors |
0.58 | 1 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcel Erné | 1 | 29 | 10.77 |
| Branimir Seselja | 2 | 63 | 10.90 |
| Andreja Tepavcevic | 3 | 143 | 22.67 |