Axiom:Lattice Ideal Axioms

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

Let $I \subseteq S$ be a non-empty subset of $S$.

$I$ is a (lattice) ideal of $S$ $I$ satisifes the axioms:

These criteria are called the (lattice) ideal axioms.