in her 1926 paper, noether extended hilbert's theorem to representations of a finite group over any field; the new case that did not follow from hilbert's work is when the characteristic of the field divides the order of the group. noether's result was later extended by william haboush to all reductive groups by his proof of the mumford conjecture. in this paper noether also introduced the "noether normalization lemma", showing that a finitely generated domain "a" over a field "k" has a set   { "x", ... , "x" }   of algebraically independent elements such that "a" is integral over   "k" ["x", ... , "x"] .