Theorems · Theorem · group theory
AddChar.map_nsmul_eq_pow
∀ {A : Type u_1} {M : Type u_3} [inst : AddMonoid A] [inst_1 : Monoid M] (ψ : AddChar A M) (n : ℕ) (x : A),
ψ (n • x) = ψ x ^ nAn additive character maps multiples by natural numbers to powers.
- Defined in
- Mathlib.Algebra.Group.AddChar
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Monoidstatement and proof · cited by 3,887
- AddMonoidstatement and proof · cited by 2,864
- AddCharstatement and proof · cited by 286
- MonoidHom.map_powproof · cited by 30
- AddChar.toMonoidHomproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- Subgroup.strictWidthInfty_pos_iffproof · cited by 5
- AddChar.mulShift_spec'proof · cited by 1
- DenseRange.addChar_eq_of_eval_one_eqproof · cited by 1
- FiniteField.two_pow_cardproof · cited by 1
- AddChar.zmod_char_ne_one_iffproof · cited by 1