Theorems · Definition · number theory
NumberField.basisOfFractionalIdeal
(K : Type u_1) →
[inst : Field K] →
[inst_1 : NumberField K] →
(I : (FractionalIdeal (nonZeroDivisors (NumberField.RingOfIntegers K)) K)ˣ) →
Module.Basis (Module.Free.ChooseBasisIndex ℤ ↥↑↑I) ℚ KA ℚ-basis of K that spans I over ℤ, see mem_span_basisOfFractionalIdeal below.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- Module.Basisstatement · cited by 1,477
- nonZeroDivisorsstatement and proof · cited by 895
- NumberFieldstatement and proof · cited by 653
- Submodule.subtypeproof · cited by 480
- FractionalIdealstatement and proof · cited by 423
- NumberField.RingOfIntegersstatement and proof · cited by 413
- LinearMap.restrictScalarsproof · cited by 215
- Module.Free.ChooseBasisIndexstatement · cited by 133
Cited by9
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.fractionalIdealLatticeBasisproof · cited by 11
- NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasisproof · cited by 3
- NumberField.mixedEmbedding.fractionalIdealLatticeBasis_applystatement and proof · cited by 2
- NumberField.det_basisOfFractionalIdeal_eq_absNormstatement and proof · cited by 1
- NumberField.fractionalIdeal_rankproof · cited by 1
- NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_normstatement and proof · cited by 1
- NumberField.basisOfFractionalIdeal_applystatement · cited by 1
- NumberField.mem_span_basisOfFractionalIdealstatement · cited by 0