Let B be a ring with 1, C be the center of B, G be a finite automorphism group of B, be the set of elements in B fixed under each element in G, and be the commutator subring of in B. Then B is called a commutator Galois extension with Galois group G if is a Galois extension with Galois group It is shown that B is a commutator Galois extension with Galois group G if and only if B is a Galois extension with Galois group G such that This generalizes a result for center Galois extensions.

Galois extensions, center Galois extensions, Azumaya Galois extensions, commutator Galois extensions, Azumaya algebras, Hirata separable extensions.