Theorems · Definition · number theory
MulChar.equiv_rootsOfUnity
(M : Type u_1) →
[inst : CommMonoid M] →
[inst_1 : Fintype M] →
[inst_2 : DecidableEq M] →
(R : Type u_2) →
[inst_3 : CommMonoidWithZero R] →
[inst_cyc : IsCyclic Mˣ] → MulChar M R ≃* ↥(rootsOfUnity (Fintype.card Mˣ) R)The group of multiplicative characters on a finite monoid M with cyclic unit group Mˣ
of order n is isomorphic to the group of nth roots of unity in the target R.
- Defined in
- Mathlib.NumberTheory.MulChar.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- Fintype.cardstatement and proof · cited by 1,386
- MulEquivstatement · cited by 1,142
- CommMonoidWithZerostatement and proof · cited by 913
- MulCharstatement and proof · cited by 186
- IsCyclicstatement and proof · cited by 122
- rootsOfUnitystatement and proof · cited by 118
- MulChar.toUnitHomproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- MulChar.exists_mulChar_orderOfproof · cited by 1