Theorems · Theorem · linear algebra

LinearMap.ker_restrict

∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
  {p : Submodule R M} {q : Submodule R₂ M₂} {f : M →ₛₗ[τ₁₂] M₂} (hf : ∀ x ∈ p, f x ∈ q),
  (f.restrict hf).ker = Submodule.comap p.subtype f.ker

Defined in

Mathlib.Algebra.Module.Submodule.Ker

Cited by

4 results in Mathlib

Foundations

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

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModule