Definition:Totally Ordered Field

Definition
Let $\struct {F, +, \circ, \preceq}$ be an ordered ring.

Let $\struct {F, +, \circ}$ be a field.

Let the ordering $\preceq$ be a total ordering.

Then $\struct {F, +, \circ, \preceq}$ is a totally ordered field.

Also known as
This is often referred to as an ordered field.

Also see

 * Field is Totally Ordered iff Ordered Compatibly with Ring Structure
 * Properties of Ordered Field