Definition:Non-Archimedean/Norm (Division Ring)

Definition
A norm $\norm {\, \cdot \,}$ on a division ring $R$ is non-Archimedean $\norm {\, \cdot \,}$ satisfies the axiom:

The pair $\struct {R, \norm {\, \cdot \, } }$ is a non-Archimedean Normed Division Ring.

If $R$ is also a commutative ring, that is, $\struct {R, \norm {\,\cdot\,}}$ is a valued field, then $\struct {R, \norm {\,\cdot\,}}$ is a non-Archimedean Valued Field.