Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:alsoKnownAs |
l-group
|
| gptkbp:definedIn |
group that is also a lattice such that the group operation is compatible with the lattice order
|
| gptkbp:example |
integer group with usual order
real numbers under addition with usual order |
| gptkbp:field |
gptkb:order_theory
abstract algebra |
| gptkbp:generalizes |
totally ordered group
|
| gptkbp:hasApplication |
gptkb:logic
measure theory ring theory |
| gptkbp:hasProperty |
every pair of elements has a least upper bound and greatest lower bound
can be Abelian or non-Abelian can be Archimedean or non-Archimedean group operation is order-preserving lattice operations distribute over group operation not every lattice-ordered group is totally ordered order is compatible with group inverse order is compatible with group multiplication order is translation-invariant positive cone forms a subsemigroup every totally ordered group is a lattice-ordered group |
| https://www.w3.org/2000/01/rdf-schema#label |
lattice-ordered group
|
| gptkbp:introduced |
gptkb:Garrett_Birkhoff
|
| gptkbp:introducedIn |
1940s
|
| gptkbp:studiedIn |
functional analysis
universal algebra |
| gptkbp:subunit |
gptkb:Riesz_space
vector lattice |
| gptkbp:bfsParent |
gptkb:vector_lattices
|
| gptkbp:bfsLayer |
8
|