---
type: "concept"
title: "Field extension"
slug: "field-extension"
language: "en"
translationGroupId: "cmraring30001qu014rpicln1"
domain: "Algebra"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

A field extension is a [[homomorphism of fields|homomorphism of fields]] $K\rightarrow L$. It is denoted as $K\subseteq L$.

##### Remarks 
- Any homomorphism of fields is injective, so $K$ can be identified with its [[Image of a map|image]] in $L$; we simply regard $K$ as a [[Subfield|subfield]] of $L$.