Theorems · Definition · number theory
rootsOfUnity
ℕ → (M : Type u_7) → [inst : CommMonoid M] → Subgroup Mˣ
rootsOfUnity k M is the subgroup of elements m : Mˣ that satisfy m ^ k = 1.
- Defined in
- Mathlib.RingTheory.RootsOfUnity.Basic
- Cited by
- 118 results in Mathlib
- Foundations
- Depth 25 from the axioms, rests on 180 definitions · uses propext
- Assumes
- CommMonoid
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.
- Set.ofPredproof · cited by 6,101
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
Cited by147
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.autToPowproof · cited by 11
- mem_rootsOfUnitystatement · cited by 10
- modularCyclotomicCharacter.toFunstatement · cited by 10
- IsPrimitiveRoot.toRootsOfUnitystatement · cited by 9
- rootsOfUnity.mkOfPowEqstatement · cited by 7
- modularCyclotomicCharacterstatement and proof · cited by 6
- SpecialLinearGroup.centerEquivRootsOfUnitystatement and proof · cited by 6
- ZMod.rootsOfUnityAddCharstatement · cited by 5
- rootsOfUnityCircleEquivstatement and proof · cited by 5
- rootsOfUnityEquivOfPrimitiveRootsstatement and proof · cited by 5
- HasEnoughRootsOfUnity.natCard_rootsOfUnitystatement and proof · cited by 5
- IsPrimitiveRoot.autToPow_specproof · cited by 5