Definition:Trivial Norm/Division Ring/Nontrivial

From ProofWiki
Jump to navigation Jump to search

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