Theorems · Theorem · commutative algebra
RingHom.LocalizationPreserves.away
∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
RingHom.LocalizationPreserves P → RingHom.LocalizationAwayPreserves fun {R S} [CommRing R] [CommRing S] => P- Defined in
- Mathlib.RingTheory.LocalProperties.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Submonoidproof · cited by 3,086
- IsLocalizationproof · cited by 636
- Submonoid.powersproof · cited by 408
- IsLocalization.Awayproof · cited by 218
- Submonoid.mapproof · cited by 190
- RingHom.LocalizationPreservesstatement and proof · cited by 13
- RingHom.LocalizationAwayPreservesstatement · cited by 12
- Submonoid.map_powersproof · cited by 10
Cited by9
Results whose statement or proof uses this declaration.
- RingHom.Smooth.propertyIsLocalproof · cited by 5
- RingHom.FormallyUnramified.propertyIsLocalproof · cited by 1
- RingHom.locally_localizationPreservesproof · cited by 0
- RingHom.QuasiFinite.propertyIsLocalproof · cited by 0
- RingHom.finitePresentation_isLocalproof · cited by 0
- RingHom.Flat.propertyIsLocalproof · cited by 0
- RingHom.finiteType_isLocalproof · cited by 0
- RingHom.localization_away_map_finiteproof · cited by 0
- RingHom.localization_away_map_finiteTypeproof · cited by 0