Theorems · Definition · linear algebra

Submodule.quotEquivOfEq

{R : Type u_1} →
  {M : Type u_2} →
    [inst : Ring R] →
      [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → (p p' : Submodule R M) → p = p' → (M ⧸ p) ≃ₗ[R] M ⧸ p'

Quotienting by equal submodules gives linearly equivalent quotients.

Defined in

Mathlib.LinearAlgebra.Quotient.Defs

Cited by

15 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModule