In mathematics, the Noether normalization lemma is a result of commutative algebra, introduced in . A simple version states that for any field k, and any finitely generated commutative k-algebra A, there exists a nonnegative integer d and algebraically independent elements y1, y2, ..., yd in A
such that A is a finitely generated module over, and hence also an integral extension of, the polynomial ring B:=k[y1, y2, ..., yd].
The integer d is uniquely determined by A: it is the Krull dimension of A. When A is an integral domain, d is then the transcendence degree of the field of fractions ...