Theorems · Definition · linear algebra

LinearMap.quotKerEquivRange

{R : Type u_1} →
  {M : Type u_2} →
    {M₂ : Type u_3} →
      [inst : Ring R] →
        [inst_1 : AddCommGroup M] →
          [inst_2 : AddCommGroup M₂] →
            [inst_3 : Module R M] → [inst_4 : Module R M₂] → (f : M →ₗ[R] M₂) → (M ⧸ f.ker) ≃ₗ[R] ↥f.range

The first isomorphism law for modules. The quotient of M by the kernel of f is linearly equivalent to the range of f.

Defined in

Mathlib.LinearAlgebra.Isomorphisms

Cited by

23 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModule