[[Field extension]]
# Separable extension

Let $L:K$ be an [[Algebraic element|algebraic extension]].
An element $\alpha \in L$ is called **separable** over $K$ iff its [[Algebraic element|minimal polynomial]] $m_{\alpha}(x) \in K[x]$ is a [[separable polynomial]]. 
The extension $L:K$ is thence called **separable** iff every element is separable. #m/def/field 

## Properties

- [[Separability of a finite extension]]

## See also

- [[Separable degree of an extension]]
- [[Discriminant of a separable extension]]

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