Theorems · Theorem · ring theory
LinearMap.injective_of_ne_zero
∀ {R : Type u_2} [inst : Ring R] {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_5}
[inst_3 : AddCommGroup N] [inst_4 : Module R N] [IsSimpleModule R M] {f : M →ₗ[R] N}, f ≠ 0 → Function.Injective ⇑f- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Ringstatement and proof · cited by 7,463
- IsSimpleModulestatement and proof · cited by 114
- LinearMap.injective_or_eq_zeroproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.bijective_or_eq_zeroproof · cited by 3