Noether normalization lemma

The noetherian normalization rate ( or noetherian Normalisierungslemma ) (after Emmy Noether ) is a structure statement from the mathematical branch of commutative algebra. In geometric language, he says that there is always a picture in an affine space is a geometric object of whose fibers are finite.

This article deals with commutative algebra. In particular, all rings considered are commutative and have an identity element. For more details see Commutative Algebra.

Formulation

It was a body and a - algebra of finite type. Then there are independent elements of algebraically, so that a finite -algebra.

Here, " algebraically independent " means that the homomorphism

From the polynomial ring is by injective.