Noether normalization lemma [SEP] named after
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", and any finitely generated commutative "k"-algebra "A", there exists a nonnegative integer "d" and algebraically independent elements "y", "y", ..., "y" in "A" 
such that "A" is a finitely generated module over the polynomial ring "S":="k"["y", "y", ...,
of "A" in "L" is a finitely generated "A"-module and is also a finitely generated "k"-algebra. The result is due to Noether and can be shown using the Noether normalization lemma as follows. It is clear that it is enough to show the assertion when "L"/"K" is either separable or purely inseparable. The separable case is noted above; thus, assume "L"/"K" is purely inseparable. By the normalization lemma, "A" is integral over the polynomial ring formula_104. Since "L"/"K"