# Definition:Normed Division Ring

## Definition

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

Let $\norm{\,\cdot\,}$ be a norm on $R$.

Then $\struct{R, \norm{\,\cdot\,} }$ is a normed division ring.

### Valued Field

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

Let $\norm{\,\cdot\,}$ be a norm on $K$.

Then $\struct{K, \norm{\,\cdot\,} }$ is a valued field.