Name
Abstract | ||
|---|---|---|
LetP, ≤� be a partially ordered set. We define the poset Boolean algebra of P , and denote it by F (P ). The set of generators of F (P )i s{xp : p ∈ P } ,a nd the set of re- lations is {xp ·xq = xp : p ≤ q} .W e say that a Bool ean algebra B is well-generated, if B has a sublattice G such that G generates B andG, ≤Gis well-founded. A well- generated algebra is superatomic. Theorem 1 LetP, ≤� be a partially ordered set. The fol- lowing are equivalent. (i) P does not contain an infinite set of pairwise incomparable elements, and P does not contain a subset isomorphic to the chain of rationalnumbers. ( ii) F (P ) is superatomic. (iii) F (P ) is well-generated. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1023/B:ORDE.0000026462.71837.18 | Order |
Keywords | Field | DocType |
poset algebras,superatomic Boolean algebras,scattered posets,well quasi orderings | Discrete mathematics,Stone's representation theorem for Boolean algebras,Combinatorics,Boolean algebras canonically defined,Incidence algebra,Field of sets,Boolean algebra (structure),Complete Boolean algebra,Mathematics,Two-element Boolean algebra,Free Boolean algebra | Journal |
Volume | Issue | ISSN |
20 | 3 | 1572-9273 |
Citations | PageRank | References |
3 | 0.94 | 1 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Uri Abraham | 1 | 56 | 13.91 |
| Robert Bonnet | 2 | 9 | 4.71 |
| Wiesław Kubiś | 3 | 3 | 1.96 |
| Matatyahu Rubin | 4 | 24 | 11.20 |