\begin{definition}[Definition:Non-Archimedean/Norm (Division Ring)/Definition 1]
Let $\struct {R, +, \circ}$ be a division ring whose zero is denoted $0_R$.
A norm $\norm {\, \cdot \,}$ on $R$ is '''non-Archimedean''' {{iff}} $\norm {\, \cdot \,}$ satisfies the axiom:
{{begin-axiom}}
{{axiom | n = \text N 4
        | lc= Ultrametric Inequality:
        | q = \forall x, y \in R
        | ml= \norm {x + y}
        | mo= \le
        | mr= \max \set {\norm x, \norm y}
}}
{{end-axiom}}
\end{definition}