---
tag: 0NXWQK2Y56
kind: concept
name: Adjoining a root of a polynomial
msc: [12F05]
sources:
  - url: https://en.wikipedia.org/wiki/Splitting_field
    locator: The field Ki[X]/(f(X))
---

## Summary

Let $f$ be an irreducible polynomial over a field $K$.
To adjoin a root of $f$ to $K$, one forms the field $K[x]/(f)$, in which the class of $x$ is a root of $f$.
The [[definition of this construction|0M893X7YY7]] gives the details.