Theorems · Definition · commutative algebra

QuotSMulTop.congr

{R : Type u_2} →
  [inst : CommRing R] →
    (r : R) →
      {M' : Type u_3} →
        {M'' : Type u_4} →
          [inst_1 : AddCommGroup M'] →
            [inst_2 : Module R M'] →
              [inst_3 : AddCommGroup M''] →
                [inst_4 : Module R M''] → (M' ≃ₗ[R] M'') → QuotSMulTop r M' ≃ₗ[R] QuotSMulTop r M''

If M' is isomorphic to M'' as R-modules, then M'⧸rM' is isomorphic to M''⧸rM''.

Defined in

Mathlib.RingTheory.QuotSMulTop

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule