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Theorems · Definition · number theory

NumberField.Units.logEmbeddingEquiv

(K : Type u_1) →
  [inst : Field K] →
    [inst_1 : NumberField K] →
      Additive ((NumberField.RingOfIntegers K)ˣ ⧸ NumberField.Units.torsion K) ≃ₗ[ℤ] ↥(NumberField.Units.unitLattice K)

The linear equivalence between (𝓞 K)ˣ ⧸ (torsion K) as an additive ℤ-module and unitLattice .

Defined in
Mathlib.NumberTheory.NumberField.Units.DirichletTheorem
Cited by
4 results in Mathlib
Foundations
Depth 308 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

NumberField.Units.basisUnitLattice · cited by 16Units.basisUnitLatticeNumberField.Units.logEmbedding_fundSystem · cited by 4Units.logEmbedding_fundSy…NumberField.Units.finrank_modTorsion · cited by 1Units.finrank_modTorsionNumberField.Units.isMaxRank_iff_closure_finiteIndex · cited by 1Units.isMaxRank_iff_closu…NumberField.Units.logEmbeddingEquiv_apply · cited by 1Units.logEmbeddingEquiv_a…Real · cited by 25697RealRingHom.id · cited by 18349RingHom.idField · cited by 7404FieldSubmodule · cited by 7192SubmoduleSubgroup · cited by 3593SubgroupLinearEquiv · cited by 3317LinearEquivUnits · cited by 2804UnitsHasQuotient.Quotient · cited by 2301HasQuotient.QuotientNumberField · cited by 653NumberFieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersAdditive · cited by 356AdditiveNumberField.Units.dirichletUnitTheorem.w₀ · cited by 72dirichletUnitTheorem.w₀LinearEquiv.ofBijective · cited by 60LinearEquiv.ofBijectiveNumberField.Units.torsion · cited by 53Units.torsionUnits.logEmbeddingEquivCITED BYCITES

Cites20

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

Cited by5

Results whose statement or proof uses this declaration.