Theorems · Theorem · commutative algebra

AdicCompletion.mk_zero_of

∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (M : Type u_4) [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  (f : AdicCompletion.AdicCauchySequence I M),
  (∃ k, ∀ n ≥ k, ∃ m ≥ n, ∃ l ≥ n, ↑f m ∈ I ^ l • ⊤) → (AdicCompletion.mk I M) f = 0

Criterion for checking that an adic Cauchy sequence is mapped to zero in the adic completion.

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

1 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule