Problem

Let F be a subfield of a field E.a. Define an evaluation homomorphismϕα1•••,αn : F[x1, •••...

Let F be a subfield of a field E.

a. Define an evaluation homomorphism

ϕα1•••,αn : F[x1, •••,xn] → E for αi ∈ E staling the analog of Theorem 22.4.

b. With E = F = ℚ, compute ϕ-3,2(x12x23 + 3x14x2).

c. Define the concept of a zero of a polynomial f(x1, •••, xn) ∈ F[x1, •••. xn] in a way analogous to the definition in the text of a zero of (x).

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Solutions For Problems in Chapter S.22