(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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a If is a nonzero homomorphism from F to Fa then it is injective a monomorphism Moreover 1F 1Fa b ...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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