Definition:Normed Division Ring
Jump to navigation
Jump to search
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.