Definition:Normed Division Ring

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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