All rings are always commutative with 10, and all homomorphisms preserve the multiplicate neutral element. 1....

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All rings are always commutative with 10, and all homomorphisms preserve the multiplicate neutral element. 1. Let F be a field with algebraic closure F. For any a € F. show that the number of homomorphisms F(a) → F compatible with the embedding of F in F is equal to the number of distinct roots of the minimal polynomial of a over F. All rings are always commutative with 10, and all homomorphisms preserve the multiplicate neutral element. 1. Let F be a field with algebraic closure F. For any a € F. show that the number of homomorphisms F(a) → F compatible with the embedding of F in F is equal to the number of distinct roots of the minimal polynomial of a over F.

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The question asks to show that for a field F with algebraic closure overlineF and any element alpha in F the number of homomorphisms from Falpha to ov... View the full answer