Separable extension

In mathematics, a separable extension of a field K is a field L containing K that can be generated by adjoining to K a set of elements α, each of which is a root of a separable polynomial over K. In that case, each β in L has a separable minimal polynomial over K.

The condition of separability is central in Galois theory. Since though all fields of characteristic 0, and all finite fields, are perfect (all extensions separable), the condition can be assumed in many contexts.