Reduction theorems for Noether's problem

Authors:
Ming-chang Kang and Bernat Plans

Journal:
Proc. Amer. Math. Soc. **137** (2009), 1867-1874

MSC (2000):
Primary 12F12, 12F20, 13A50, 11R32, 14E08

DOI:
https://doi.org/10.1090/S0002-9939-09-09608-7

Published electronically:
January 6, 2009

MathSciNet review:
2480265

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be any field, and be a finite group. Let act on the rational function field by -automorphisms and . Denote by the fixed field. Noether's problem asks whether is rational (= purely transcendental) over . We will give several reduction theorems for solving Noether's problem. For example, let be a direct product of finite groups. Theorem. Assume that is rational over . Then is rational over . In particular, if is rational (resp. retract rational) over , so is over .

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Additional Information

**Ming-chang Kang**

Affiliation:
Department of Mathematics and Taida Institute of Mathematical Sciences, National Taiwan University, Taipei, Taiwan

Email:
kang@math.ntu.edu.tw

**Bernat Plans**

Affiliation:
Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Diagonal, 647, 08028 Barcelona, Spain

Email:
bernat.plans@upc.edu

DOI:
https://doi.org/10.1090/S0002-9939-09-09608-7

Keywords:
Noether's problem,
rationality problem,
retract rational.

Received by editor(s):
August 29, 2007

Received by editor(s) in revised form:
March 7, 2008

Published electronically:
January 6, 2009

Additional Notes:
The second-named author was partially supported by MTM2006-04895 (Ministerio de Educación y Ciencia) and by 2005SGR00557 (Generalitat de Catalunya).

Communicated by:
Martin Lorenz

Article copyright:
© Copyright 2009
American Mathematical Society