Theorems · Theorem · commutative algebra

LinearMap.ker_eq_range_of_comp_eq_id

∀ {R : Type u_1} [inst : Semiring R] {M : Type u_10} {P : Type u_11} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : AddCommGroup P] [inst_4 : Module R P] {f : M →ₗ[R] P} {g : P →ₗ[R] M},
  f ∘ₗ g = LinearMap.id → f.ker = (LinearMap.id - g ∘ₗ f).range

Defined in

Mathlib.Algebra.Module.Submodule.Range

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommGroupModuleAddCommGroupModule