The Noether normalization lemma says, in geometric terms, that every affine scheme X of finite type over a field k has a finite surjective morphism to affine space A_n_ over k, where n is the dimension of X. Likewise, every projective scheme X over a field has a finite surjective morphism to projective space P_n_, where n is the dimension of X. 
Noether Normalization
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integrally closed
Tags: #NT/algebraic #CA Refs: normalization Noether normalization
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finite type
Noether normalization: if \(X\in {\mathsf{Aff}}{\mathsf{Sch}}_{/ {k}} ^{\mathrm{ft}}\), then there is a finite surjective morphism $X\twoheadrightarrow{\mathbf{A}}^d_{/ {k}} $ where \(d\coloneqq\dim X\).
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2021-04-29_2 Yves Andre On the canonical, fpqc and finite topologies
Noether normalization can show some finite coverings of \({\mathbf{A}}^3_{/k}\) are not \({\operatorname{fppf}}\) coverings.