Noether normalization lemma

In mathematics, the Noether normalization lemma is a result of commutative algebra, introduced by Emmy Noether in 1926. It states that for any field k {\displaystyle k} , and any finitely generated commutative k-algebra A {\displaystyle A} , there exist elements y 1 , y 2 , … , y d {\displaystyle y_{1},y_{2},\ldots ,y_{d}} in A {\displaystyle A} that are algebraically independent over k {\displaystyle k} and such that A {\displaystyle A} is a finitely generated module over the polynomial ring S = k [ y 1 , y 2 , … , y d ] {\displaystyle S=k[y_{1},y_{2},\ldots ,y_{d}]} .

Source: Wikipedia — Noether normalization lemma (CC BY-SA 4.0)

Noether normalization lemma

In mathematics, the Noether normalization lemma is a result of commutative algebra, introduced by Emmy Noether in 1926. It states that for any field k {\displaystyle k} , and any finitely generated commutative k-algebra A {\displaystyle A} , there exist elements y 1 , y 2 , … , y d {\displaystyle y_{1},y_{2},\ldots ,y_{d}} in A {\displaystyle A} that are algebraically independent over k {\displaystyle k} and such that A {\displaystyle A} is a finitely generated module over the polynomial ring S = k [ y 1 , y 2 , … , y d ] {\displaystyle S=k[y_{1},y_{2},\ldots ,y_{d}]} .

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Source: Wikipedia "Noether normalization lemma" · CC BY-SA 4.0

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