Theorems · Definition · commutative algebra

AdicCompletion.IsAdicCauchy

{R : Type u_1} →
  [inst : CommRing R] → Ideal R → (M : Type u_4) → [inst_1 : AddCommGroup M] → [Module R M] → (ℕ → M) → Prop

A sequence ℕ → M is an I-adic Cauchy sequence if for every m ≤ n, f m ≡ f n modulo I ^ m • ⊤.

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

19 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule