Theorems · Definition · group theory
AddChar.mulShift
{R : Type u_1} → {M : Type u_2} → [inst : Ring R] → [inst_1 : CommMonoid M] → AddChar R M → R → AddChar R MDefine the multiplicative shift of an additive character.
This satisfies mulShift ψ a x = ψ (a * x).
- Defined in
- Mathlib.Algebra.Group.AddChar
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- RingCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- CommMonoidstatement and proof · cited by 2,264
- AddCharstatement and proof · cited by 286
- AddMonoidHom.mulLeftproof · cited by 23
- AddChar.compAddMonoidHomproof · cited by 5
Cited by27
Results whose statement or proof uses this declaration.
- AddChar.IsPrimitiveproof · cited by 22
- AddChar.mulShift_applystatement · cited by 9
- gaussSum_mulShiftstatement · cited by 5
- AddChar.sum_mulShiftproof · cited by 2
- AddChar.zmod_char_primitive_of_eq_one_only_at_zeroproof · cited by 2
- AddChar.inv_mulShiftstatement and proof · cited by 2
- AddChar.mulShift_mulstatement and proof · cited by 2
- AddChar.mulShift_mulShiftstatement and proof · cited by 2
- AddChar.mulShift_onestatement and proof · cited by 2
- AddChar.mulShift_zerostatement and proof · cited by 2
- mul_gaussSum_inv_eq_gaussSumproof · cited by 1
- AddChar.pow_mulShiftstatement and proof · cited by 1