---
tag: 0KXQKX9P63
kind: concept
name: Splitting field
msc: [12F05]
sources:
  - url: https://en.wikipedia.org/wiki/Splitting_field
    locator: lead section
same_as:
  wikidata: Q1996100
  wikipedia: Splitting field
---

## Summary

A splitting field of a polynomial over a field is a smallest extension field over which the polynomial splits into linear factors.
It is generated by the roots of the polynomial.
The [[definition of a splitting field|02NZZ1J0FH]] states it.