Field extension

Separable extension

Let 𝐿 :𝐾 be an algebraic extension. An element 𝛼 ∈𝐿 is called separable over 𝐾 iff its minimal polynomial 𝑚𝛼(𝑥) ∈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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