---
tag: 0H628RSGWX
kind: concept
name: Algebraic element
msc: [12F05]
sources:
  - url: https://en.wikipedia.org/wiki/Algebraic_element
    locator: lead section
same_as:
  wikidata: Q162608
  wikipedia: Algebraic element
---

## Summary

Let $L/K$ be a field extension.
An element of $L$ is algebraic over $K$ if it is a root of a nonzero polynomial with coefficients in $K$.
The [[definition of an algebraic element|0NPW1DWECM]] states it.