2005/10/02 | 阿廷符号[Artin Symbol]
类别(∑〖数学〗) | 评论(0) | 阅读(21) | 发表于 10:33
Given a number field , a Galois extension field , and prime ideals of and of unramified over , there exists a unique element of the Galois group such that for every element of ,
(1)

where is the norm of the prime ideal in .

The symbol is called an Artin symbol. If is an Abelian extension of , the Artin symbol depends only on the prime ideal of lying under , so it may be written as . In this case, the Artin symbol can be generalized as follows. Let be an ideal of with prime factorization
(2)

Then the Artin symbol is defined by
(3)


Then the Artin symbol is defined by
0

评论Comments

日志分类
首页[1408]
∑〖数学〗[349]
Ω〖物理〗[357]
¤〖天文〗[343]
℃〖化学〗[359]