Complemented lattice

In the mathematical discipline of order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0.Complements need not be unique. A relatively complemented lattice is a lattice such that every interval [c, d], viewed as a bounded lattice in its own right, is a complemented lattice. In distributive lattices, complements are unique. Every complemented distributive lattice has a unique orthocomplementation and is in fact a Boolean algebra.

Complemented lattice

In the mathematical discipline of order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0.Complements need not be unique. A relatively complemented lattice is a lattice such that every interval [c, d], viewed as a bounded lattice in its own right, is a complemented lattice. In distributive lattices, complements are unique. Every complemented distributive lattice has a unique orthocomplementation and is in fact a Boolean algebra.