Étale field extensions #
Mathlib's Algebra.FormallyEtale.of_isSeparable shows that a separable field extension is
formally étale. This file adds the finiteness condition: a finite separable field extension is
étale (Algebra.Etale.of_isSeparable).
theorem
Algebra.Etale.of_isSeparable
(K : Type u_1)
(L : Type u_2)
[Field K]
[Field L]
[Algebra K L]
[Module.Finite K L]
[Algebra.IsSeparable K L]
:
Etale K L
A finite separable field extension is étale.