(a) If F is a field and : F Fa (ring) homomorphism, then =...

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(a) If F is a field and σ : F → Fa (ring) homomorphism, then σ = 0 or σ is a monomorphism. If σ ≠ 0, then σ(1F) = 1F,

(b) The set Aut F of all field automorphisms F → F forms a group under the operation of composition of functions.

(c) AutKF, the set of all K-automorphisms of F is a subgroup of Aut F.

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