Theorems · Theorem · linear algebra

LinearMap.injective_domRestrict_iff

∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Ring R] [inst_1 : Ring R₂]
  [inst_2 : AddCommGroup M] [inst_3 : AddCommGroup M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
  {f : M →ₛₗ[τ₁₂] M₂} {S : Submodule R M}, Function.Injective ⇑(f.domRestrict S) ↔ Disjoint S f.ker

Defined in

Mathlib.Algebra.Module.Submodule.Ker

Cited by

2 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingRingAddCommGroupAddCommGroupModuleModule