Theorems · Theorem · number theory
MulChar.mulEquiv_units
∀ (M : Type u_1) (R : Type u_2) [inst : CommMonoid M] [inst_1 : CommRing R] [Finite M] [HasEnoughRootsOfUnity R (Monoid.exponent Mˣ)], Nonempty (MulChar M R ≃* Mˣ)
The group of R-valued multiplicative characters on a finite commutative monoid M is
(noncanonically) isomorphic to its unit group Mˣ when R is a ring that has enough roots
of unity.
- Defined in
- Mathlib.NumberTheory.MulChar.Duality
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Finitestatement and proof · cited by 3,029
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- MulEquivstatement · cited by 1,142
- Nonempty.someproof · cited by 340
- MulCharstatement · cited by 186
- Monoid.exponentstatement and proof · cited by 128
- HasEnoughRootsOfUnitystatement and proof · cited by 56
- MulEquiv.transproof · cited by 53
- MulChar.mulEquivToUnitHomproof · cited by 7
- CommGroup.monoidHom_mulEquiv_of_hasEnoughRootsOfUnityproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- DirichletCharacter.mulEquiv_unitsproof · cited by 1
- MulChar.card_eq_card_units_of_hasEnoughRootsOfUnityproof · cited by 0