Theorems · Theorem · commutative algebra
CharacterModule.dual_surjective_of_injective
∀ {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] (f : A →ₗ[R] B),
Function.Injective ⇑f → Function.Surjective ⇑(CharacterModule.dual f)- Defined in
- Mathlib.Algebra.Module.CharacterModule
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- AddCircleproof · cited by 189
- LinearMap.toAddMonoidHomproof · cited by 101
- CharacterModulestatement · cited by 26
- CharacterModule.dualstatement · cited by 13
- Module.Baer.extension_property_addMonoidHomproof · cited by 1
- Module.Baer.of_divisibleproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CharacterModule.exists_character_apply_ne_zero_of_ne_zeroproof · cited by 1
- CharacterModule.dual_surjective_iff_injectiveproof · cited by 1