Definition:Semilattice

Definition
Let $\struct {S, \circ}$ be a semigroup.

Then $\struct {S, \circ}$ is called a semilattice $\circ$ is a commutative and idempotent operation.

Thus an algebraic structure is a semilattice it satisfies the semilattice axioms:

Also see

 * Definition:Lattice