Definition:Prime Ideal (Order Theory)

Definition
Let $I$ be an ideal in an ordered set $S$.

Then $I$ is a prime ideal in $S$ $S \setminus I$ is a filter.

Also see

 * Prime Ideal in Lattice

Special cases

 * Definition:Prime Ideal of Ring, as shown at Prime Ideal of Ring iff Prime Ideal in Lattice of Ideals