Definition:Prime Element (Order Theory)

Definition
Let $\left({S, \wedge, \preceq}\right)$ be a meet semilattice.

Let $p \in S$.

Then $p$ is prime (element)
 * $\forall x, y \in S: \left({ x \wedge y \preceq p \implies x \preceq p \lor y \preceq p }\right)$