I am reading Szamuely´s book "Galois groups and fundamental groups" and I am somewhat confused about how he is defining an etale algebra:
A finite dimensional k-algebra A is etale (over k) if it is isomorphic to a finite direct product of separable extensions of k.
Now I have seen several other definitions regarding an etale algebra, namely it being isomorphic to a finite direct product of FINITE separable extensions of k or even distinguishing etale algebras and finite algebras for this specific point.
For Theorem 1.5.4 he then uses the wording of an finite etale algebra. Does he now refer to the definition with finite separable extensions, because that is what I think is needed for the proof.