Definition:Trivial Norm/Division Ring

Definition
Let $\left({R, +, \circ}\right)$ be a division ring, and denote its zero by $0_R$.

Then the map $\left \Vert{\cdot}\right \Vert: R \to \R_{\ge 0}$ given by:


 * $\left\Vert{x}\right\Vert = \begin{cases}

0 & : \text{if $x = 0_R$}\\ 1 & : \text{otherwise} \end{cases}$

defines a norm on $R$, called the trivial norm.

Also known as
Some authors refer to this norm as the trivial absolute value.

Also see

 * Trivial Norm on Division Ring is Norm


 * Definition:Standard Discrete Metric