Theorems · Theorem · commutative algebra

surjective_of_localized_span

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N] (s : Set R),
  Ideal.span s = ⊤ →
    ∀ (f : M →ₗ[R] N),
      (∀ (r : ↑s), Function.Surjective ⇑((LocalizedModule.map (Submonoid.powers ↑r)) f)) → Function.Surjective ⇑f

Defined in

Mathlib.RingTheory.LocalProperties.Exactness

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModule