Theorems · Theorem · linear algebra

LinearEquiv.ker_comp

∀ {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] {module_M : Module R M} {module_M₂ : Module R₂ M₂} {module_M₃ : Module R₃ M₃}
  {σ₁₂ : R →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃} [inst_6 : RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] {σ₃₂ : R₃ →+* R₂}
  {re₂₃ : RingHomInvPair σ₂₃ σ₃₂} {re₃₂ : RingHomInvPair σ₃₂ σ₂₃} (e'' : M₂ ≃ₛₗ[σ₂₃] M₃) (l : M →ₛₗ[σ₁₂] M₂),
  (↑e'' ∘ₛₗ l).ker = l.ker

Defined in

Mathlib.Algebra.Module.Submodule.Ker

Cited by

11 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringSemiringAddCommMonoidAddCommMonoidAddCommMonoidRingHomCompTriple