Theorems · Theorem · commutative algebra

RingHom.StableUnderComposition.stableUnderCompositionWithLocalizationAway

∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
  (RingHom.StableUnderComposition fun {R S} [CommRing R] [CommRing S] => P) →
    (RingHom.HoldsForLocalizationAway fun {R S} [CommRing R] [CommRing S] => P) →
      RingHom.StableUnderCompositionWithLocalizationAway fun {R S} [CommRing R] [CommRing S] => P

Defined in: Mathlib.RingTheory.LocalProperties.Basic
Cited by: 7 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

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

CommRingstatement and proof · cited by 17,173
Algebraproof · cited by 11,388
RingHomstatement and proof · cited by 10,189
Algebra.algebraMapproof · cited by 4,706
IsLocalization.Awayproof · cited by 218
RingHom.StableUnderCompositionstatement and proof · cited by 26
RingHom.HoldsForLocalizationAwaystatement and proof · cited by 16
RingHom.StableUnderCompositionWithLocalizationAwaystatement · cited by 6

Cited by7

Results whose statement or proof uses this declaration.

RingHom.Smooth.propertyIsLocalproof · cited by 5
RingHom.FormallyUnramified.propertyIsLocalproof · cited by 1
RingHom.isStandardSmooth_stableUnderCompositionWithLocalizationAwayproof · cited by 1
RingHom.Flat.propertyIsLocalproof · cited by 0
RingHom.QuasiFinite.propertyIsLocalproof · cited by 0
RingHom.finiteType_isLocalproof · cited by 0
RingHom.finitePresentation_isLocalproof · cited by 0