\begin{definition}[Definition:Non-Archimedean/Norm (Division Ring)/Definition 2]
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:
{{:Axiom:Non-Archimedean Norm Axioms}}
\end{definition}