Theorems · Theorem · number theory
DirichletCharacter.mulEquiv_units
∀ (R : Type u_1) [inst : CommRing R] (n : ℕ) [NeZero n] [HasEnoughRootsOfUnity R (Monoid.exponent (ZMod n)ˣ)], Nonempty (DirichletCharacter R n ≃* (ZMod n)ˣ)
The group of Dirichlet characters mod n with values in a ring R that has enough
roots of unity is (noncanonically) isomorphic to (ZMod n)ˣ.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Unitsstatement and proof · cited by 2,804
- MulEquivstatement · cited by 1,142
- ZModstatement and proof · cited by 1,024
- DirichletCharacterstatement · cited by 161
- Monoid.exponentstatement and proof · cited by 128
- HasEnoughRootsOfUnitystatement and proof · cited by 56
- MulChar.mulEquiv_unitsproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- DirichletCharacter.card_eq_totient_of_hasEnoughRootsOfUnityproof · cited by 1