Theorems · Definition · number theory

NumberField.fractionalIdealBasis

(K : Type u_1) →
  [inst : Field K] →
    [inst_1 : NumberField K] →
      (I : FractionalIdeal (nonZeroDivisors (NumberField.RingOfIntegers K)) K) →
        Module.Basis (Module.Free.ChooseBasisIndex ℤ ↥↑I) ℤ ↥↑I

A ℤ-basis of a fractional ideal.

Defined in: Mathlib.NumberTheory.NumberField.FractionalIdeal
Cited by: 3 results in Mathlib
Foundations: Depth 187 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.

Cites10

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
Submodulestatement · cited by 7,192
Module.Basisstatement · cited by 1,477
nonZeroDivisorsstatement and proof · cited by 895
NumberFieldstatement and proof · cited by 653
FractionalIdealstatement and proof · cited by 423
NumberField.RingOfIntegersstatement and proof · cited by 413
Module.Free.ChooseBasisIndexstatement · cited by 133
FractionalIdeal.coeToSubmodulestatement and proof · cited by 130
Module.Free.chooseBasisproof · cited by 121

Cited by4

Results whose statement or proof uses this declaration.

NumberField.basisOfFractionalIdealproof · cited by 8
NumberField.basisOfFractionalIdeal_applystatement and proof · cited by 1
NumberField.det_basisOfFractionalIdeal_eq_absNormproof · cited by 1
NumberField.mem_span_basisOfFractionalIdealproof · cited by 0