Lüroth定理[Lüroth's Theorem] - 达人(其实～我是卧底，来自外星)

2004/11/24 | Lüroth定理[Lüroth's Theorem]
类别(∑〖数学〗) | 评论(0) | 阅读(47) | 发表于 16:56: A theorem that can be stated either in the language of abstract algebraic curves or transcendental extensions.

For an abstract algebraic curve, if x and y are nonconstant rational functions of a parameter, the curve so defined has curve genus 0. Furthermore, x and y may be expressed rationally in terms of a parameter which is rational in them (Coolidge 1959, p. 246).

For simple transcendental extensions, all proper extensions of a field F which are contained in a simple transcendental extension of F are also simple transcendental. In particular, if K is an intermediate field between F and the field F(x) of rational functions over F, then for some nonconstant rational function g(x) (van der Waerden 1966, p. 198).; 0