Theorems · Theorem · commutative algebra
CharacterModule.dual_zero
∀ {R : Type uR} [inst : CommRing R] {A : Type uA} [inst_1 : AddCommGroup A] {B : Type uB} [inst_2 : AddCommGroup B]
[inst_3 : Module R A] [inst_4 : Module R B], CharacterModule.dual 0 = 0- Defined in
- Mathlib.Algebra.Module.CharacterModule
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- map_zeroproof · cited by 1,614
- LinearMap.extproof · cited by 844
- CharacterModulestatement and proof · cited by 26
- CharacterModule.dualstatement · cited by 13
- CharacterModule.extproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- CharacterModule.surjective_of_dual_injectiveproof · cited by 1