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- Principal_ideal_theorem abstract "This article is about the Hauptidealsatz of class field theory. You may be seeking Krull's principal ideal theorem, also known as Krull's Hauptidealsatz, in commutative algebraIn mathematics, the principal ideal theorem of class field theory, a branch of algebraic number theory, is the statement that 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 is a principal ideal αOL, for OL the ring of integers of L and some element α in it. In other terms, extending ideals gives a mapping on the class group of K, to the class group of L, which sends all ideal classes to the class of a principal ideal. The phenomenon has also been called principalization, or sometimes capitulation. It was conjectured by David Hilbert, and was the last remaining aspect of his programme on class fields to be completed, around 1930.The question was reduced to a piece of finite group theory by Emil Artin. That involved the transfer. The required result was proved by Philipp Furtwängler.".
- Principal_ideal_theorem wikiPageID "3136164".
- Principal_ideal_theorem wikiPageRevisionID "555822687".
- Principal_ideal_theorem hasPhotoCollection Principal_ideal_theorem.
- Principal_ideal_theorem subject Category:Group_theory.
- Principal_ideal_theorem subject Category:Homological_algebra.
- Principal_ideal_theorem subject Category:Ideals.
- Principal_ideal_theorem subject Category:Theorems_in_algebraic_number_theory.
- Principal_ideal_theorem type Abstraction100002137.
- Principal_ideal_theorem type Cognition100023271.
- Principal_ideal_theorem type Communication100033020.
- Principal_ideal_theorem type Content105809192.
- Principal_ideal_theorem type Idea105833840.
- Principal_ideal_theorem type Ideal105923696.
- Principal_ideal_theorem type Ideals.
- Principal_ideal_theorem type Message106598915.
- Principal_ideal_theorem type Proposition106750804.
- Principal_ideal_theorem type PsychologicalFeature100023100.
- Principal_ideal_theorem type Statement106722453.
- Principal_ideal_theorem type Theorem106752293.
- Principal_ideal_theorem type TheoremsInAlgebraicNumberTheory.
- Principal_ideal_theorem type TheoremsInNumberTheory.
- Principal_ideal_theorem comment "This article is about the Hauptidealsatz of class field theory.".
- Principal_ideal_theorem label "Principal ideal theorem".
- Principal_ideal_theorem label "Théorème de l'idéal principal".
- Principal_ideal_theorem sameAs Théorème_de_l'idéal_principal.
- Principal_ideal_theorem sameAs m.08trtd.
- Principal_ideal_theorem sameAs Q3527196.
- Principal_ideal_theorem sameAs Q3527196.
- Principal_ideal_theorem sameAs Principal_ideal_theorem.
- Principal_ideal_theorem wasDerivedFrom Principal_ideal_theorem?oldid=555822687.
- Principal_ideal_theorem isPrimaryTopicOf Principal_ideal_theorem.