Theorems · Theorem · number theory
MulChar.apply_mem_rootsOfUnity
∀ {R : Type u_1} {R' : Type u_2} [inst : CommRing R] [inst_1 : CommRing R'] [inst_2 : Fintype Rˣ] (a : Rˣ)
{χ : MulChar R R'}, (MulChar.equivToUnitHom χ) a ∈ rootsOfUnity (Fintype.card Rˣ) R'The values of a multiplicative character on R are nth roots of unity, where n = #Rˣ.
- Defined in
- Mathlib.NumberTheory.MulChar.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Equivstatement · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- Fintype.cardstatement and proof · cited by 1,386
- map_powproof · cited by 503
- MulCharstatement and proof · cited by 186
- rootsOfUnitystatement · cited by 118
- MonoidHom.map_oneproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- MulChar.star_eq_invproof · cited by 0