\begin{definition}[Definition:Semilattice]
Let $\struct {S, \circ}$ be a semigroup.
Then $\struct {S, \circ}$ is called a '''semilattice''' {{iff}} $\circ$ is a commutative and idempotent operation.
Thus an algebraic structure is a '''semilattice''' {{iff}} it satisfies the '''semilattice axioms''':
{{:Axiom:Semilattice Axioms}}
\end{definition}