Theorems · Definition · commutative algebra

IsAdicComplete.StrictMono.extend

{R : Type u_1} →
  [inst : CommRing R] →
    {I : Ideal R} →
      {M : Type u_4} →
        [inst_1 : AddCommGroup M] →
          [inst_2 : Module R M] →
            {N : Type u_5} →
              [inst_3 : AddCommGroup N] →
                [inst_4 : Module R N] →
                  {a : ℕ → ℕ} → StrictMono a → ((n : ℕ) → M →ₗ[R] N ⧸ I ^ a n • ⊤) → (n : ℕ) → M →ₗ[R] N ⧸ I ^ n • ⊤

Instead of providing all M →ₗ[R] N ⧸ (I ^ n • ⊤), one can just provide M →ₗ[R] N ⧸ (I ^ (a n) • ⊤) for a strictly increasing sequence a n to recover all M →ₗ[R] N ⧸ (I ^ n • ⊤).

Defined in

Mathlib.RingTheory.AdicCompletion.Basic

Cited by

6 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule