Theorems · Theorem · number theory
MulChar.map_nonunit
∀ {R : Type u_1} [inst : CommMonoid R] {R' : Type u_2} [inst_1 : CommMonoidWithZero R'] (χ : MulChar R R') {a : R},
¬IsUnit a → χ a = 0- Defined in
- Mathlib.NumberTheory.MulChar.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
- Assumes
- CommMonoidCommMonoidWithZero
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
- CommMonoidstatement and proof · cited by 2,264
- IsUnitstatement and proof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- MulCharstatement and proof · cited by 186
- MulChar.map_nonunit'proof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- MulChar.extproof · cited by 16
- MulChar.map_zeroproof · cited by 10
- MulChar.pow_apply'proof · cited by 7
- DirichletCharacter.norm_le_oneproof · cited by 7
- MulChar.inv_applyproof · cited by 2
- MulChar.sum_one_eq_card_unitsproof · cited by 2
- MulChar.apply_ne_zero_iffproof · cited by 2
- quadraticChar_exists_neg_one'proof · cited by 2
- DirichletCharacter.modZero_eq_deltaproof · cited by 1
- MulChar.isQuadratic_iff_sq_eq_oneproof · cited by 1
- gaussSum_mulShift_of_isPrimitiveproof · cited by 1
- MulChar.exists_apply_ne_one_of_hasEnoughRootsOfUnityproof · cited by 1