Definition:Join Semilattice Ideal

Definition
Let $\struct {S, \vee, \preceq}$ be a join semilattice.

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

Then $I$ is an ideal of $S$ $I$ satisifies the ideal axioms:

Also see

 * Definition:Ideal (Order Theory)


 * User:Leigh.Samphier/OrderTheory/Lattice Ideal iff Ordered Set Ideal