Theorems · Theorem · commutative algebra

RingHom.OfLocalizationSpanTarget.ofIsLocalization

∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
  (RingHom.OfLocalizationSpanTarget fun {R S} [CommRing R] [CommRing S] => P) →
    (RingHom.RespectsIso fun {R S} [CommRing R] [CommRing S] => P) →
      ∀ {R S : Type u} [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S) (s : Set S),
        Ideal.span s = ⊤ →
          (∀ (r : ↑s), ∃ T x x_1, ∃ (_ : IsLocalization.Away (↑r) T), P ((algebraMap S T).comp f)) → P f

Defined in

Mathlib.RingTheory.LocalProperties.Basic

Cited by

1 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRing