---
tag: 0VX9EP2GS8
kind: concept
name: Minimal polynomial (field theory)
aliases: [minimal-polynomial]
msc: [12F05]
sources:
  - url: https://en.wikipedia.org/wiki/Minimal_polynomial_(field_theory)
    locator: lead section
same_as:
  wikidata: Q2242730
  wikipedia: Minimal polynomial (field theory)
---

## Summary

Let $a$ be algebraic over a field $K$.
The minimal polynomial of $a$ over $K$ is the monic polynomial of smallest degree in $K[x]$ that has $a$ as a root.
The [[definition of the minimal polynomial|0GK1WB9R98]] states it.