Prove that if A is the field of all algebraic numbers (Section 32), then [A : iQJ is
Chapter 45, Problem 45.6(choose chapter or problem)
Prove that if A is the field of all algebraic numbers (Section 32), then [A : iQJ is infinite.(Suggestion: Use Eisenstein'5 irreducibility criterion, Theorem 43.6, to prove that, for eachpositive integer n, there is a polynomial of degree n that is irreducible over iQ. Why does thatsuffice?)
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