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principal ideal theorem : ウィキペディア英語版
principal ideal theorem

In mathematics, the principal ideal theorem of class field theory, a branch of algebraic number theory says that extending ideals gives a mapping on the class group of an algebraic number field to the class group of its Hilbert class field, which sends all ideal classes to the class of a principal ideal. The phenomenon has also been called ''principalization'', or sometimes ''capitulation''.
==Formal statement==
For any algebraic number field ''K'' and any ideal ''I'' of the ring of integers of ''K'', if ''L'' is the Hilbert class field of ''K'', then
:IO_L\
is a principal ideal α''O''''L'', for ''O''''L'' the ring of integers of ''L'' and some element α in it.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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