Theorems · Theorem · ring theory
LinearMap.injective_or_eq_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), Function.Injective ⇑f ∨ f = 0- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 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 · 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
- Bot.botproof · cited by 4,720
- LinearMap.kerproof · cited by 848
- IsSimpleModulestatement and proof · cited by 114
- LinearMap.ker_eq_botproof · cited by 92
- IsSimpleOrder.eq_bot_or_eq_topproof · cited by 32
- LinearMap.ker_eq_topproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- Submodule.map_le_isotypicComponentproof · cited by 2
- LinearMap.injective_of_ne_zeroproof · cited by 1
- Representation.IsIrreducible.injective_or_eq_zeroproof · cited by 0