Let F be a field and let φ : F → F be a ring isomorphism....

Let F be a field and let φ : F → F be a ring isomorphism. Define Fix φ to be Fix φ = {a ∈ F | φ(a) = a}. That is, Fix φ is the set of all elements of F that are fixed under φ. Prove that Fix φ is a field. (b) Define φ : C → C by φ(a + bi) = a − bi. Take for granted that φ is a ring isomorphism (we proved this in class at some point). Find Fix φ.

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Colby Messinger answered 1 year ago

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