Definition:Non-Archimedean/Norm (Division Ring)/Definition 1

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

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

Also see

 * Leigh.Samphier/Sandbox/Equivalence of Definitions of Non-Archimedean Division Ring Norm