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.

单词	Principal ideal theorem
释义	Principal ideal theorem 英语百科 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.
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