# Wikipedia Authors - Algebraic extension (Highlights) ![rw-book-cover|256](https://readwise-assets.s3.amazonaws.com/static/images/article2.74d541386bbf.png) ## Highlights - In [mathematics](https://en.wikipedia.org/wiki/Mathematics), an **algebraic extension** is a [field extension](https://en.wikipedia.org/wiki/Field_extension) *L*/*K* such that every element of the larger [field](https://en.wikipedia.org/wiki/Field_(mathematics)) L is [algebraic](https://en.wikipedia.org/wiki/Algebraic_element) over the smaller field K; that is, every element of L is a root of a non-zero [polynomial](https://en.wikipedia.org/wiki/Polynomial) with coefficients in K. ([View Highlight](https://read.readwise.io/read/01hsvy2eb0yv6b2ad3kwhm9bx9)) ^698010808 #definition