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ZioX
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Homework Statement
I want to show that the homomorphism phi:A(X)->k+k given by taking f(x_1,...,x_n)-> (f(P_1),f(P_2)) is surjective. That is, given any (a,b) in k^2 (with addition and multiplication componentwise) I want to find a polynomial that has the property that f(P_1)=a and f(P_2)=b.
The actual question is to show that if we take the coordinate ring of two points in k^n then the coordinate ring is isomorphic to k+k (direct product).
Homework Equations
The Attempt at a Solution
I have everything but surjectivity. phi is obviously an injective homomorphism (ker phi = {0 polynomial}).
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