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.

Also see

• Definition:Norm on Division Ring
• Definition:Normed Ring
• Definition:Valued Field