Definition:Trivial Norm/Division Ring

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

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


 * $\norm x = \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


 * Nontrivial Norm on Division Ring