Definition:Ordered Integral Domain/Trichotomy Law

Definition
Let $\left({D, +, \times, \le}\right)$ be an ordered integral domain, where $\le$ is the ordering induced by the positivity property $P$.

The property:
 * $\forall a \in D: P \left({a}\right) \lor P \left({-a}\right) \lor a = 0_D$

is known as the trichotomy law. That is:
 * Every element of $D$ is either positive, or negative, or zero.