Definition:Separable Extension

Definition

Let $K$ be a field.

Let $L/K$ be an algebraic field extension.

Then $L/K$ is a separable extension if and only if every $\alpha\in L$ is separable over $K$.

That is:

For every $\alpha \in L$, its minimal polynomial over $K$ is separable.

Also see

• Definition:Normal Extension
• Definition:Galois Extension
• Definition:Inseparable Field Extension
• Definition:Purely Inseparable Extension

• Results about separable extensions can be found here.

Sources

• Weisstein, Eric W. "Separable Extension." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SeparableExtension.html
• This article incorporates material from separable on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.