Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
Lattice (order theory) |
| gptkbp:characterizedBy |
Absence of M3 and N5 sublattices
|
| gptkbp:definedIn |
gptkb:Distributive_law
|
| gptkbp:example |
gptkb:Power_set_lattice
Set of natural numbers ordered by divisibility Totally ordered set |
| gptkbp:field |
gptkb:Mathematics
gptkb:Order_theory |
| gptkbp:generalizes |
gptkb:algebra
gptkb:Heyting_algebra |
| gptkbp:hasProperty |
Every pair of elements has a greatest lower bound (meet)
Every sublattice of a distributive lattice is distributive Every Boolean algebra is a distributive lattice Every chain is distributive Join distributes over meet Meet distributes over join Not every lattice is distributive Product of distributive lattices is distributive Intersection of distributive lattices is distributive Every pair of elements has a least upper bound (join) Every finite distributive lattice is isomorphic to the lattice of lower sets of a finite poset |
| gptkbp:hasSpecialCase |
gptkb:Lattice
|
| https://www.w3.org/2000/01/rdf-schema#label |
Distributive lattice
|
| gptkbp:namedFor |
gptkb:Richard_Dedekind
|
| gptkbp:studiedBy |
Birkhoff, Garrett
|
| gptkbp:used_in |
gptkb:logic
gptkb:Abstract_algebra Computer science |
| gptkbp:bfsParent |
gptkb:Posets
gptkb:Lattice |
| gptkbp:bfsLayer |
6
|