Lattice

In mathematics, a lattice is a partially ordered set (also called a PoSet) in which any two elements have a unique supremum (the elements' least upper bound; called their join) and an infimum (greatest lower bound; called their meet).

Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. The following was taken from Mathworld:

An algebra $$\langle L; \wedge, \vee \rangle$$ is called a lattice if $$L$$ is a nonempty set, $$\wedge$$ and $$\vee$$ are binary operations on $$L$$, both $$\wedge$$ and $$\vee$$ are idempontent, commutative and associateive, and they satisfy the AbsorptionLaw.