# Definition:Ordered Ring

## Definition

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

Let $\preceq$ be an ordering compatible with the ring structure of $\struct {R, +, \circ}$.

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

### Totally Ordered Ring

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

If the ordering $\preceq$ is a total ordering, then $\struct {R, +, \circ, \preceq}$ is a totally ordered ring.

## Also see

• Results about ordered rings can be found here.