Definition:Lattice

Also defined as
Some sources refer to a bounded lattice as a lattice.

This comes down to insisting that $\vee$ and $\wedge$ admit identity elements.

Also denoted as
In particular in the context of order theory, it is common to omit $\vee$ and $\wedge$ in the notation for a lattice.

That is, one then writes $\struct {S, \preceq}$ in place of $\struct {S, \vee, \wedge, \preceq}$.

Also see

 * Equivalence of Definitions of Lattice


 * Definition:Bounded Lattice
 * Definition:Join Semilattice
 * Definition:Meet Semilattice
 * Definition:Semilattice
 * Definition:Complete Lattice
 * Definition:Lattice (Ordered Set): a specific instantiation of a lattice in the context of an ordered set