Theorems · Definition · number theory
NumberField.Units.torsion
(K : Type u_1) → [inst : Field K] → Subgroup (NumberField.RingOfIntegers K)ˣ
The torsion subgroup of the group of units.
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- NumberField.RingOfIntegersstatement and proof · cited by 413
- CommGroup.torsionproof · cited by 16
Cited by65
Results whose statement or proof uses this declaration.
- NumberField.Units.torsionOrderproof · cited by 17
- NumberField.IsCMField.unitsMulComplexConjInvstatement · cited by 9
- NumberField.Units.basisModTorsionstatement and proof · cited by 4
- NumberField.Units.logEmbeddingEquivstatement · cited by 4
- NumberField.Units.logEmbedding_fundSystemproof · cited by 4
- NumberField.IsCMField.indexRealUnitsproof · cited by 4
- Ideal.torsionMapQuotstatement and proof · cited by 3
- NumberField.Units.closure_fundSystem_sup_torsion_eq_topstatement and proof · cited by 2
- NumberField.Units.exist_unique_eq_mul_prodstatement and proof · cited by 2
- NumberField.Units.finiteIndex_iff_sup_torsion_finiteIndexstatement and proof · cited by 2
- NumberField.Units.logEmbeddingQuotstatement · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.integerSetEquivstatement and proof · cited by 2