(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(1_F) = 1_F,

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

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 16, 2023 03:56 AM

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

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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

Algebra Graduate Texts In Mathematics 73

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