Definition:Ordered Integral Domain/Definition 1

Definition
An ordered integral domain is an integral domain $\struct {D, +, \times}$ which has a strict positivity property $P$:

An ordered integral domain can be denoted:
 * $\struct {D, +, \times \le}$

where $\le$ is the total ordering induced by the strict positivity property.

Also see

 * Equivalence of Definitions of Ordered Integral Domain