Theorems · Theorem · number theory
HasEnoughRootsOfUnity.natCard_rootsOfUnity
∀ (M : Type u_1) [inst : CommMonoid M] (n : ℕ) [NeZero n] [HasEnoughRootsOfUnity M n], Nat.card ↥(rootsOfUnity n M) = n
If M satisfies HasEnoughRootsOfUnity, then the group of nth roots of unity
in M (is cyclic and) has order n.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- Units.valproof · cited by 1,966
- Nat.cardstatement · cited by 844
- Subtype.propproof · cited by 505
- IsPrimitiveRootproof · cited by 356
- orderOfproof · cited by 324
- IsUnit.unitproof · cited by 252
- Monoid.exponentproof · cited by 128
- rootsOfUnitystatement and proof · cited by 118
- HasEnoughRootsOfUnitystatement and proof · cited by 56
Cited by5
Results whose statement or proof uses this declaration.
- cyclotomicCharacter.toZModPow_toFunstatement and proof · cited by 2
- cyclotomicCharacter.toFun_specproof · cited by 1
- cyclotomicCharacter.toZModPowstatement · cited by 1
- IsCyclic.monoidHom_equiv_selfproof · cited by 1
- cyclotomicCharacter.continuousproof · cited by 0