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    Graduate How Many Homomorphisms Can Be Calculated Between Different Fields?

    a) I agree b) I am thinking that a homomorphism f will be uniquely defined by f(x) Prove it. But 0 = f(0) = f(x^7 - 3) = f(x)^7 - f(3) = f(x)^7 - 3 and how many solutions does this have? But I suppose we have to bear in mind that this zero is k(x^8 + 4x^5 - 6x + 2) for any k c) similar d) Using...