希尔伯特类域[Hilbert Class Field][2005-11-16] iamet 发表在 ∑〖数学〗
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 .
, 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 
.
of 
over 
is equal to the class number of 
.