Definition:Trivial Norm/Division Ring/Nontrivial
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Definition
A norm $\norm {\, \cdot \,}$ on a division ring $R$ is nontrivial if and only if it is not trivial.
That is, if and only if:
- $\exists x \in R: \norm x \ne 0$ and $\norm x \ne 1$
Sources
- 1997: Fernando Q. Gouvea: p-adic Numbers: An Introduction: $\S2.1$ Absolute Values on a Field, Definition $2.1.1$, Example $2$
- 2007: Svetlana Katok: p-adic Analysis Compared with Real: $\S1.2$ Normed Fields, Definition $1.5$