The Noether Normalization Lemma

This is a standard result in commutative algebra (cf. for example, Zariski-Samuel, vol. 2, Ch. 7, 7). However there is a fairly straightforward and geometric proof, using only the Noether normalization lemma and based on the Norm, so I think it is worthwhile proving the algebraic version too. This proof is due to J. Tate. 

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