---
tag: 0TNS65QB87
kind: concept
name: Prime subfield
aliases: [prime-field]
msc: ["12E99"]
sources:
  - url: https://en.wikipedia.org/wiki/Field_(mathematics)
    locator: Subfields and prime fields
---

## Summary

The prime subfield of a field is its smallest subfield.
It is $\mathbb{Q}$ or $\mathbb{F}_p$, up to isomorphism, by the characteristic.
The [[definition of the prime subfield|0VPFBAY7MW]] gives the details.