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Let F be a field and let ? : F ? F be a ring...

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Advance Math

Let F be a field and let ? : F ? F be a ring isomorphism. DefineFix ? to be Fix ? = {a ? F | ?(a) = a}. That is, Fix ? is the setof all elements of F that are fixed under ?. Prove that Fix ? is afield.   (b) Define ? : C ? C by ?(a + bi) = a ? bi. Takefor granted that ? is a ring isomorphism (we proved this in classat some point). Find Fix ?.

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