How to show an affine variety in $\mathbb{A}^{n}$ either has finite cardinality or equal to that of $k$? I do not know how to solve this via elementary methods.
How to show an affine variety in $\mathbb{A}^{n}$ either has finite cardinality or equal to that of $k$?
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algebraic-geometry
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0Sorry for the confusion, clarified; also by Noether normalization lemma this is immediate. – 2012-11-12