---- > [!definition] Definition. ([[characteristic of a field]]) > The **characteristic** of a [[field]] $\mathbb{F}$ is the [[order of an element in a group|order]] of the element $1$, as an element of the additive [[group]] $(\mathbb{F},+)$. If said order is not finite, then the [[field]] is said to have **characteristic zero**. Or see [[characteristic of a ring]]. > [!basicexample] > The characteristic of a [[prime field]] $\mathbb{F}_{p}$ is $p$. [[Subfield]]s of [[complex numbers]] have characteristic zero. ---- #### ---- #### References > [!backlink] > ```d[](field.md) TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```