Theorems · Definition · number theory

NumberField.integralBasis

(K : Type u_1) →
  [inst : Field K] →
    [inst_1 : NumberField K] → Module.Basis (Module.Free.ChooseBasisIndex ℤ (NumberField.RingOfIntegers K)) ℚ K

A basis of K over ℚ that is also a basis of 𝓞 K over ℤ.

Defined in: Mathlib.NumberTheory.NumberField.Basic
Cited by: 25 results in Mathlib
Foundations: Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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

Cites8

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

Fieldstatement and proof · cited by 7,404
Module.Basisstatement · cited by 1,477
nonZeroDivisorsproof · cited by 895
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement · cited by 413
Module.Free.ChooseBasisIndexstatement · cited by 133
Module.Basis.localizationLocalizationproof · cited by 15
NumberField.RingOfIntegers.basisproof · cited by 12

Cited by26

Results whose statement or proof uses this declaration.

NumberField.canonicalEmbedding.latticeBasisproof · cited by 7
NumberField.canonicalEmbedding.latticeBasis_applystatement · cited by 7
NumberField.integralBasis_applystatement · cited by 6
NumberField.mixedEmbedding.latticeBasis_applystatement · cited by 4
NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisproof · cited by 4
NumberField.absNorm_differentIdealproof · cited by 4
NumberField.coe_discrstatement · cited by 4
NumberField.mem_span_integralBasisstatement · cited by 3
NumberField.basisMatrix_eq_embeddingsMatrixReindexstatement and proof · cited by 2
NumberField.discr_ne_zeroproof · cited by 2
NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_normproof · cited by 1
NumberField.inverse_basisMatrix_mulVec_eq_reprstatement and proof · cited by 1