Theorems · Definition · commutative algebra

AdicCompletion.ofLinearEquiv

{R : Type u_1} →
  [inst : CommRing R] →
    (I : Ideal R) →
      (M : Type u_4) →
        [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → [IsAdicComplete I M] → M ≃ₗ[R] AdicCompletion I M

When M is I-adic complete, the canonical map from M to its I-adic completion is a linear equivalence.

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

5 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleIsAdicComplete