Definition:Lattice Ideal

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

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

Also see

 * Equivalence of Definitions of Lattice Ideal
 * Definition:Join Semilattice Ideal
 * Definition:Ideal (Order Theory)
 * Join Semilattice Ideal iff Ordered Set Ideal
 * Definition:Lattice Filter