Noetherian Normalization Theorem
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.