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Additional
principal ideal theorem
English Wikipedia - The Free Encyclopedia
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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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