Theorems · Definition · number theory

NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv

(K : Type u_1) →
  [inst : Field K] →
    [inst_1 : NumberField K] →
      ↑(NumberField.mixedEmbedding.fundamentalCone.integerSet K) ≃
        { I // Submodule.IsPrincipal ↑I } × ↥(NumberField.Units.torsion K)

The equivalence between integerSet K and the product of the set of nonzero principal ideals of K and the torsion of K.

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone
Cited by: 2 results in Mathlib
Foundations: Depth 338 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites23

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Equivstatement · cited by 8,337
Fieldstatement and proof · cited by 7,404
Set.Elemstatement and proof · cited by 7,166
Idealstatement · cited by 4,748
Subgroupstatement · cited by 3,593
Submonoidstatement · cited by 3,086
Unitsstatement and proof · cited by 2,804
nonZeroDivisorsstatement · cited by 895
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement and proof · cited by 413
Equiv.transproof · cited by 337
NumberField.mixedEmbedding.mixedSpacestatement · cited by 239

Cited by3

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNormproof · cited by 2
NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fstproof · cited by 0
NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv_apply_fststatement · cited by 0