Theorems · Theorem · linear algebra

LinearMap.ker_comp_of_ker_eq_bot

∀ {R : Type u_1} {R₂ : Type u_2} {R₃ : Type u_3} {M : Type u_5} {M₂ : Type u_7} {M₃ : Type u_8} [inst : Semiring R]
  [inst_1 : Semiring R₂] [inst_2 : Semiring R₃] [inst_3 : AddCommMonoid M] [inst_4 : AddCommMonoid M₂]
  [inst_5 : AddCommMonoid M₃] [inst_6 : Module R M] [inst_7 : Module R₂ M₂] [inst_8 : Module R₃ M₃] {τ₁₂ : R →+* R₂}
  {τ₂₃ : R₂ →+* R₃} {τ₁₃ : R →+* R₃} [inst_9 : RingHomCompTriple τ₁₂ τ₂₃ τ₁₃] (f : M →ₛₗ[τ₁₂] M₂) {g : M₂ →ₛₗ[τ₂₃] M₃},
  g.ker = ⊥ → (g ∘ₛₗ f).ker = f.ker

Defined in

Mathlib.Algebra.Module.Submodule.Ker

Cited by

6 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleRingHomCompTriple