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What does it mean for a subset of $\mathbb{C}[x_1,\dots,x_n]$ to be algebraically independent?

Particularly I'd like to know the formulation thereof which concerns the kernel of a surjective ring isomorphism.

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I don't know why this was downvoted, but since the guy left no reason and it doesn't seems like a bad question I upvote it. –  Belgi May 8 '12 at 14:46
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Let $\{f_i\}$ be a family of elements. You can define $\mathbf C[\{y_i\}] \to \mathbf C[x_1, \ldots, x_n]$ by sending $y_i \mapsto f_i$. What can you say about the kernel? –  Dylan Moreland May 8 '12 at 14:50

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