Definition:Non-Archimedean/Norm (Division Ring)/Definition 2

Definition
Let $\struct {R, +, \circ}$ be a division ring whose zero is denoted $0_R$.

A non-Archimedean norm on $R$ is a mapping from $R$ to the non-negative reals:
 * $\norm {\,\cdot\,}: R \to \R_{\ge 0}$

satisfying the non-Archimedean norm axioms:

Also see

 * Definition:Non-Archimedean/Norm (Division Ring)/Definition 1
 * Equivalence of Definitions of Non-Archimedean Division Ring Norm