Definition:Ordered Field

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

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

Then $\struct {R, +, \circ, \preceq}$ is an ordered field.

Also defined as
The term ordered field is frequently used to refer to what we call a totally ordered field.

Sources defining partially ordered field vary in their definitions.

Some require only a field which is an ordered ring, while others impose further restrictions.