Definition:Absolute Value/Ordered Integral Domain

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

Then for all $a \in D$, the absolute value of $a$ is defined as:


 * $\left\vert{a}\right\vert = \begin{cases}

a & : 0 \le a \\ -a & : a < 0 \end{cases}$

Also see

 * Integers form Ordered Integral Domain
 * Rational Numbers form Ordered Integral Domain
 * Real Numbers form Ordered Integral Domain

from which it follows that the definition for numbers is compatible with this.