# Wikipedia Authors - Algebraic extension (Highlights) ![rw-book-cover|256](https://readwise-assets.s3.amazonaws.com/static/images/article2.74d541386bbf.png) ## Metadata **Review**:: [readwise.io](https://readwise.io/bookreview/39028803) **Source**:: #from/readwise #from/reader **Zettel**:: #zettel/fleeting **Status**:: #x **Authors**:: [[Wikipedia Authors]] **Full Title**:: Algebraic extension **Category**:: #articles #readwise/articles **Category Icon**:: 📰 **URL**:: [en.wikipedia.org](https://en.wikipedia.org/wiki/Algebraic_extension) **Host**:: [[en.wikipedia.org]] **Highlighted**:: [[2024-03-25]] **Created**:: [[2024-03-27]] ## 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