Theorems · Definition · number theory
NumberField.Units.IsMaxRank
{K : Type u_1} →
[inst : Field K] →
[inst_1 : NumberField K] → (Fin (NumberField.Units.rank K) → (NumberField.RingOfIntegers K)ˣ) → PropA family of units is of maximal rank if its image by logEmbedding is linearly independent
over ℝ.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 301 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realproof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Unitsstatement and proof · cited by 2,804
- NumberFieldstatement and proof · cited by 653
- LinearIndependentproof · cited by 560
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Additive.ofMulproof · cited by 155
- NumberField.Units.rankstatement and proof · cited by 46
- NumberField.Units.logEmbeddingproof · cited by 25
Cited by14
Results whose statement or proof uses this declaration.
- NumberField.Units.regOfFamilyproof · cited by 12
- NumberField.Units.basisOfIsMaxRankstatement and proof · cited by 9
- NumberField.Units.isMaxRank_fundSystemstatement · cited by 4
- NumberField.Units.regOfFamily_of_isMaxRankstatement and proof · cited by 4
- NumberField.Units.regOfFamily_eq_det'proof · cited by 3
- NumberField.Units.regOfFamily_eq_zerostatement and proof · cited by 3
- NumberField.Units.basisOfIsMaxRank_applystatement and proof · cited by 3
- NumberField.Units.regOfFamily_posstatement and proof · cited by 2
- NumberField.Units.isMaxRank_iff_closure_finiteIndexstatement and proof · cited by 1
- NumberField.Units.regOfFamily_div_regOfFamilystatement and proof · cited by 1
- NumberField.Units.regOfFamily_ne_zerostatement and proof · cited by 1
- NumberField.Units.span_basisOfIsMaxRankstatement and proof · cited by 1