Theorems · Inductive type · number theory
MulChar
(R : Type u_1) → [CommMonoid R] → (R' : Type u_2) → [CommMonoidWithZero R'] → Type (max u_1 u_2)
Define a structure for multiplicative characters.
A multiplicative character from a commutative monoid R to a commutative monoid with zero R'
is a homomorphism of (multiplicative) monoids that sends non-units to zero.
- Defined in
- Mathlib.NumberTheory.MulChar.Basic
- Cited by
- 186 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 3 definitions · uses no axioms
- Assumes
- CommMonoidCommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement · cited by 2,264
- CommMonoidWithZerostatement · cited by 913
Cited by220
Results whose statement or proof uses this declaration.
- DirichletCharacterproof · cited by 161
- quadraticCharstatement · cited by 34
- gaussSumstatement and proof · cited by 29
- ZMod.χ₄statement · cited by 27
- MulChar.equivToUnitHomstatement · cited by 20
- MulChar.IsQuadraticstatement and proof · cited by 18
- MulChar.extstatement and proof · cited by 16
- MulChar.ringHomCompstatement and proof · cited by 15
- MulChar.toUnitHomstatement and proof · cited by 14
- jacobiSumstatement and proof · cited by 14
- ZMod.χ₈statement · cited by 14
- MulChar.map_nonunitstatement and proof · cited by 13
Showing the 200 most cited of 220.