Theorems · Definition · number theory
NumberField.Units.rank
(K : Type u_1) → [inst : Field K] → [NumberField K] → ℕ
The unit rank of the number field K, it is equal to card (InfinitePlace K) - 1.
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 141 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.
Cites4
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
- Fintype.cardproof · cited by 1,386
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlaceproof · cited by 604
Cited by55
Results whose statement or proof uses this declaration.
- NumberField.Units.fundSystemstatement and proof · cited by 23
- NumberField.Units.basisUnitLatticestatement · cited by 16
- NumberField.Units.IsMaxRankstatement and proof · cited by 12
- NumberField.Units.regOfFamilystatement and proof · cited by 12
- NumberField.mixedEmbedding.fundamentalCone.equivFinRankstatement · cited by 10
- NumberField.Units.basisOfIsMaxRankstatement and proof · cited by 9
- NumberField.Units.regulator_eq_regOfFamily_fundSystemproof · cited by 7
- NumberField.Units.equivFinRankstatement · cited by 5
- NumberField.Units.basisModTorsionstatement · cited by 4
- NumberField.Units.isMaxRank_fundSystemproof · cited by 4
- NumberField.Units.logEmbedding_fundSystemstatement and proof · cited by 4
- NumberField.Units.regOfFamily_of_isMaxRankstatement and proof · cited by 4