Remark. Complements may not exist. If is a non-trivial chain, then no element (other than and ) has a complement. This also shows that if is a complement of a non-trivial element , then and form an antichain.
An element in a bounded lattice is complemented if it has a complement. A complemented lattice is a bounded lattice in which every element is complemented.
In a complemented lattice, there may be more than one complement corresponding to each element. Two elements are said to be related, or perspective if they have a common complement. For example, the following lattice is complemented.
Note that none of the non-trivial elements have unique complements. Any two non-trivial elements are related via the third.
|Date of creation||2013-03-22 15:02:25|
|Last modified on||2013-03-22 15:02:25|
|Last modified by||CWoo (3771)|
|Defines||related elements in lattice|