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.

If $\struct {R, +, \circ}$ is a field then $\struct{R, \norm{\,\cdot\,} }$ is called a valued field.

Also see

 * Definition:Norm on Division Ring


 * Definition:Normed Ring