Theorems · Definition · linear algebra

Submodule.Quotient.restrictScalarsEquiv

{R : Type u_1} →
  {M : Type u_2} →
    [inst : Ring R] →
      [inst_1 : AddCommGroup M] →
        [inst_2 : Module R M] →
          (S : Type u_3) →
            [inst_3 : Ring S] →
              [inst_4 : SMul S R] →
                [inst_5 : Module S M] →
                  [inst_6 : IsScalarTower S R M] → (P : Submodule R M) → (M ⧸ Submodule.restrictScalars S P) ≃ₗ[S] M ⧸ P

The quotient of P as an S-submodule is the same as the quotient of P as an R-submodule, where P : Submodule R M.

Defined in

Mathlib.LinearAlgebra.Quotient.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

RingAddCommGroupModuleRingSMulModuleIsScalarTower