Theorems · Theorem · commutative algebra

RingHom.OfLocalizationSpan.mk

∀ (P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop),
  (RingHom.RespectsIso fun {R S} [CommRing R] [CommRing S] => P) →
    (∀ {R S : Type u} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (s : Set R),
        Ideal.span s = ⊤ →
          (∀ r ∈ s, P (algebraMap (Localization.Away r) (TensorProduct R (Localization.Away r) S))) →
            P (algebraMap R S)) →
      RingHom.OfLocalizationSpan fun {R S} [CommRing R] [CommRing S] => P

Defined in: Mathlib.RingTheory.LocalProperties.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites30

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Setstatement and proof · cited by 53,352
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
RingHomstatement and proof · cited by 10,189
Top.topstatement and proof · cited by 9,680
Set.Elemproof · cited by 7,166
Idealstatement · cited by 4,748
Algebra.algebraMapstatement and proof · cited by 4,706
TensorProductstatement and proof · cited by 2,545
TensorProduct.tmulproof · cited by 1,182
Ideal.spanstatement and proof · cited by 948

Cited by1

Results whose statement or proof uses this declaration.

RingHom.finiteType_ofLocalizationSpanproof · cited by 0