Definition of Semilattice. Meaning of Semilattice. Synonyms of Semilattice

- In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset...
- equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras...
- arrangement of planes. The intersection semilattice L(A) is a meet semilattice and more specifically is a geometric semilattice. If the arrangement is linear or...
- theorem for commutative semigroups in terms of semilattices. A semilattice (or more precisely a meet-semilattice) (L, ≤) is a partially ordered set where every...
- pairs have a join is a join-semilattice. Dually, a partially ordered set in which all pairs have a meet is a meet-semilattice. A partially ordered set that...
- called a closed sublattice of L. The terms complete meet-semilattice or complete join-semilattice is another way to refer to complete lattices since arbitrary...
- least lattices, but the concept can in fact reasonably be generalized to semilattices as well. Probably the most common type of distributivity is the one defined...
- generalized Boolean algebra, while (B, ∨, 0) is a generalized Boolean semilattice. Generalized Boolean lattices are exactly the ideals of Boolean lattices...
- cannot be a lattice (or even a meet semilattice), since by definition, every two elements in a lattice (or meet semilattice) must have a common lower bound...
- (contrast partially ordered sets, which need not be directed). Join-semilattices (which are partially ordered sets) are directed sets as well, but not...