Let F be a field and let p(x) be irreducible over F. If E
Chapter 17, Problem 31E(choose chapter or problem)
Problem 31E
Let F be a field and let p(x) be irreducible over F. If E is a field that contains F and there is an element a in E such that p(a) = 0, show that the mapping Φ: F[x] → E given by f(x) → f(a) is a ring homomorphism with kernel . (This exercise is referred to in Chapter 20.)
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