I'm having some difficulty with this homework problem:
If $A=K[x_1,...,x_n]$, $K$ a field and $a_1,a_2,...,a_n $ $\in K$. The ideal $m=<x_1-a_1,...,x_n-a_n>$ is maximal.
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Hint: Consider the evaluation map $K[x_1,\ldots,x_n]\to K$ which takes a polynomial $f(x_1,\ldots,x_n)$ to the point in $K$ given by $f(a_1,\ldots,a_n)$.
Jared
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does the trick lie here that $K[x_1,x_2,...,x_n]/ker\phi$ isomorphic to $K$ correct me if I am wrong @Jared – Learnmore Nov 18 '14 at 04:13
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@learnmore: You got it! – Jared Nov 18 '14 at 07:27
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@Jared You are totally correct. Thanks. – Santiago Montoya Nov 18 '14 at 16:29