Theorems · Theorem · number theory
DirichletCharacter.changeLevel_injective
∀ {R : Type u_1} [inst : CommMonoidWithZero R] {n m : ℕ} [NeZero m] (hm : n ∣ m),
Function.Injective ⇑(DirichletCharacter.changeLevel hm)The changeLevel map is injective (except in the degenerate case m = 0).
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZeroNeZero
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
- MonoidHomstatement · cited by 3,629
- Unitsproof · cited by 2,804
- ZModstatement and proof · cited by 1,024
- CommMonoidWithZerostatement and proof · cited by 913
- MonoidHom.compproof · cited by 469
- DirichletCharacterstatement and proof · cited by 161
- DirichletCharacter.changeLevelstatement and proof · cited by 29
- ZMod.unitsMapproof · cited by 24
- MulChar.equivToUnitHomproof · cited by 20
- MulChar.extproof · cited by 16
- MulChar.coe_equivToUnitHomproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- DirichletCharacter.conductor_dvd_of_mem_conductorSetproof · cited by 2
- DirichletCharacter.conductor_changeLevelproof · cited by 1
- DirichletCharacter.changeLevel_eq_one_iffproof · cited by 1
- DirichletCharacter.primitiveCharacter_changeLevel_applyproof · cited by 1
- DirichletCharacter.FactorsThrough.existsUniqueproof · cited by 0