---
tag: 05NAS7AGMZ
kind: concept
name: Field generated by adjoining elements
aliases: [field-adjunction]
msc: [12F05]
sources:
  - url: https://en.wikipedia.org/wiki/Field_extension
    locator: Extension field
---

## Summary

For a field extension $L/K$ and a subset $S$ of $L$, the field $K(S)$ is the smallest subfield of $L$ that contains $K$ and $S$.
The [[definition of $K(S)$|0MA5B744K3]] states it.