\begin{definition}[Definition:Ordered Integral Domain/Definition 1]
An '''ordered integral domain''' is an integral domain $\struct {D, +, \times}$ which has a strict positivity property $P$:
{{:Definition:Strict Positivity Property}}
An '''ordered integral domain''' can be denoted:
:$\struct {D, +, \times \le}$
where $\le$ is the total ordering induced by the strict positivity property.
\end{definition}