Theorems · Theorem · commutative algebra
CharacterModule.eq_zero_of_character_apply
∀ {A : Type uA} [inst : AddCommGroup A] {a : A}, (∀ (c : CharacterModule A), c a = 0) → a = 0- Defined in
- Mathlib.Algebra.Module.CharacterModule
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
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 and proof · cited by 62,936
- AddCommGroupstatement and proof · cited by 12,871
- AddSubgroup.zmultiplesstatement · cited by 493
- AddCirclestatement · cited by 189
- CharacterModulestatement and proof · cited by 26
- CharacterModule.exists_character_apply_ne_zero_of_ne_zeroproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CharacterModule.surjective_of_dual_injectiveproof · cited by 1
- CharacterModule.dual_surjective_iff_injectiveproof · cited by 1