Definition:Ordered Integral Domain/Trichotomy Law

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

The property:
 * $\forall a \in D: \map P a \lor \map P {-a} \lor a = 0_D$

is known as the trichotomy law. That is:


 * Every element of $D$ is either strictly positive, or strictly negative, or zero.