Integral Element - Noether's Normalization Lemma

Noether's Normalization Lemma

Noether's normalisation lemma is a theorem in commutative algebra. Given a field K and a finitely generated K-algebra A, the theorem says it is possible to find elements y₁, y₂, ..., y_m in A that are algebraically independent over K such that A is finite (and hence integral) over B = K. Thus the extension K ⊂ A can be written as a composite K ⊂ B ⊂ A where K ⊂ B is a purely transcendental extension and B ⊂ A is finite.