Theorems · Theorem · number theory
mem_rootsOfUnity
∀ {M : Type u_1} [inst : CommMonoid M] (k : ℕ) (ζ : Mˣ), ζ ∈ rootsOfUnity k M ↔ ζ ^ k = 1- Defined in
- Mathlib.RingTheory.RootsOfUnity.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 26 from the axioms · 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.
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- rootsOfUnitystatement · cited by 118
Cited by10
Results whose statement or proof uses this declaration.
- mem_rootsOfUnity'proof · cited by 3
- Complex.norm_eq_one_of_mem_rootsOfUnityproof · cited by 3
- NumberField.Units.rootsOfUnity_eq_torsionproof · cited by 2
- MulChar.apply_mem_algebraAdjoin_of_pow_eq_oneproof · cited by 2
- Complex.mem_rootsOfUnityproof · cited by 1
- MulChar.apply_mem_rootsOfUnityproof · cited by 1
- MulChar.exists_mulChar_orderOfproof · cited by 1
- MulChar.apply_mem_rootsOfUnity_orderOfproof · cited by 1
- NumberField.Units.rootsOfUnity_eq_oneproof · cited by 0
- mem_rootsOfUnity_prime_pow_mul_iff'proof · cited by 0