希尔伯特类域[Hilbert Class Field] - 达人(其实～我是卧底，来自外星)

2005/11/16 | 希尔伯特类域[Hilbert Class Field]
类别(∑〖数学〗) | 评论(0) | 阅读(24) | 发表于 21:00: Given a number field , there exists a unique maximal unramified Abelian extension of which contains all other unramified Abelian extensions of . This finite field extension is called the Hilbert class field of . By a theorem of class field theory, the Galois group is isomorphic to the class group of and for every subgroup of , there exists a unique unramified Abelian extension of contained in such that .
The degree of over is equal to the class number of .; 0