field characteristic

Definition

For a field $k$ the characteristic of $k$ is

$$\text{char }k=\{\begin{array}{l}\min \{n\in \mathbb{Z}|\underset{n-\text{times}}{\underbrace{1+1+\cdots +1}}\}\\ 0\text{if above does not exist}\end{array}$$

Examples

• $\text{char}{\mathbb{Z}}_2=0$

• $\text{char}\mathbb{R}=0$

• $\text{char}\mathbb{C}=0$