---
tag: 0ZXZ82FTX2
kind: concept
name: Finite field
msc: ["12E20"]
sources:
  - url: https://en.wikipedia.org/wiki/Finite_field
    locator: lead section
same_as:
  wikidata: Q603880
  wikipedia: Finite field
---

## Summary

A finite field is a field with a finite number of elements.
For each prime power $q$ there is exactly one finite field of order $q$, up to isomorphism, and there are no other finite fields.
The [[definition of a finite field|08RTDHX1SK]] states it.