Theorems · Definition · commutative algebra

AdicCompletion.congr

{R : Type u_1} →
  [inst : CommRing R] →
    (I : Ideal R) →
      {M : Type u_2} →
        [inst_1 : AddCommGroup M] →
          [inst_2 : Module R M] →
            {N : Type u_3} →
              [inst_3 : AddCommGroup N] →
                [inst_4 : Module R N] → (M ≃ₗ[R] N) → AdicCompletion I M ≃ₗ[AdicCompletion I R] AdicCompletion I N

A linear equiv induces a linear equiv on adic completions.

Defined in

Mathlib.RingTheory.AdicCompletion.Functoriality

Cited by

2 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule