Noetherian Normalization Theorem

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The Noetherian normalization theorem (or Noetherian normalization lemma ) (after Emmy Noether ) is a structural statement from the mathematical sub-area of commutative algebra . In geometric language, it means that there is always a mapping of a geometric object in an affine space, the fibers of which are finite.

This article is about commutative algebra. In particular, all rings under consideration are commutative and have a one element. For more details, see Commutative Algebra .

formulation

It is one body and one - algebra of finite type . Then there are algebraically independent elements , so that a finite -algebra, i.e. all over . One can choose for the degree of transcendence .

"Algebraically independent" means that the homomorphism

from the polynomial after is injective.

See also