Kersten, I. Noether’s problem and normalization. (English) Zbl 1055.12501 Jahresber. Dtsch. Math.-Ver. 100, No. 1, 3-22 (1998). The author provides a very well-written survey of the current status of the work on Noether’s problem. Let \(k\) be a field, \(k(x_1,\cdots,x_n)\) the rational function field in \(n\) variables, and \(G\) a finite group acting as automorphisms of \(k(x_1,\cdots,x_n)\) and permuting the variables, then the question studied is whether the fixed field of the automorphisms is also a rational function field in \(n\) variables. She nicely presents the work of several researchers, a. o. Noether, Saltman, Swan, Lenstra, Colliot-Thélène, Sansuc, up to the present state. A large bibliography of 85 items is added. Reviewer: Olaf Ninnemann (Berlin) Cited in 5 Documents MSC: 12F10 Separable extensions, Galois theory 12F20 Transcendental field extensions 01A60 History of mathematics in the 20th century Keywords:generic Galois extensions; Hilbert’s fourteenth problem; Noether normalization × Cite Format Result Cite Review PDF