Theorems · Theorem · commutative algebra

Module.exists_localizedMap_away_surjective_of_localizedMap_atPrime_surjective

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_3}
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] [Module.Finite R M] (p : Ideal R) [inst_6 : p.IsPrime]
  (φ : N →ₗ[R] M),
  Function.Surjective ⇑((LocalizedModule.map p.primeCompl) φ) →
    ∃ a ∉ p, Function.Surjective ⇑((LocalizedModule.map (Submonoid.powers a)) φ)

Defined in

Mathlib.RingTheory.Support

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleModule.FiniteIdeal.IsPrime