Definition:Well-Ordered Integral Domain/Definition 1

Definition

Let $\struct {D, +, \times \le}$ be an ordered integral domain whose zero is $0_D$.

$\struct {D, +, \times \le}$ is a well-ordered integral domain if and only if the ordering $\le$ is a well-ordering on the set $P$ of (strictly) positive elements of $D$.

Also see

• Equivalence of Definitions of Well-Ordered Integral Domain

• Results about well-ordered integral domains can be found here.