Definition:Ordered Integral Domain/Trichotomy Law

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Definition

Let $\struct {D, +, \times, \le}$ be an ordered integral domain.

Let $P$ be the strict positivity property on $D$


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.


Sources