Documentation

Mathlib.NumberTheory.NumberField.ClassNumber

Class numbers of number fields #

This file defines the class number of a number field as the (finite) cardinality of the class group of its ring of integers. It also proves some elementary results on the class number.

Main definitions #

noncomputable def NumberField.classNumber (K : Type u_1) [Field K] [NumberField K] :

The class number of a number field is the (finite) cardinality of the class group.

Equations
Instances For

    The class number of a number field is 1 iff the ring of integers is a PID.

    To show that the ring of integer of a number field is a PID it is enough to show that all ideals above any (natural) prime p smaller than Minkowski bound are principal.