Definition:Complemented Lattice

Definition

Let $\struct {S, \vee, \wedge, \preceq}$ be a bounded lattice.

Suppose that every $a \in S$ admits a complement.

Then $\struct {S, \vee, \wedge, \preceq}$ is called a complemented lattice.

Also see

• Definition:Complement (Lattice Theory)

Linguistic Note

The word complement comes from the idea of complete-ment, it being the thing needed to complete something else.

It is a common mistake to confuse the words complement and compliment.

Usually the latter is mistakenly used when the former is meant.