Theorems · Theorem · number theory

NumberField.integralBasis_apply

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  (i : Module.Free.ChooseBasisIndex ℤ (NumberField.RingOfIntegers K)),
  (NumberField.integralBasis K) i =
    (algebraMap (NumberField.RingOfIntegers K) K) ((NumberField.RingOfIntegers.basis K) i)

Defined in: Mathlib.NumberTheory.NumberField.Basic
Cited by: 6 results in Mathlib
Foundations: Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites12

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

DFunLike.coestatement · cited by 62,936
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
Algebra.algebraMapstatement · cited by 4,706
Module.Basisstatement · cited by 1,477
nonZeroDivisorsproof · cited by 895
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement and proof · cited by 413
Module.Free.ChooseBasisIndexstatement and proof · cited by 133
NumberField.integralBasisstatement · cited by 25
NumberField.RingOfIntegers.basisstatement and proof · cited by 12
Module.Basis.localizationLocalization_applyproof · cited by 6

Cited by6

Results whose statement or proof uses this declaration.

NumberField.canonicalEmbedding.latticeBasis_applyproof · cited by 7
NumberField.absNorm_differentIdealproof · cited by 4
NumberField.mixedEmbedding.latticeBasis_applyproof · cited by 4
NumberField.basisMatrix_eq_embeddingsMatrixReindexproof · cited by 2
NumberField.conj_basisMatrixproof · cited by 1
NumberField.discr_eq_discr_of_algEquivproof · cited by 1