Theorems · Theorem · commutative algebra
RingHom.IsStableUnderBaseChange.localizationPreserves
∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
RingHom.IsStableUnderBaseChange P → RingHom.LocalizationPreserves fun {R S} [CommRing R] [CommRing S] => P- Defined in
- Mathlib.RingTheory.LocalProperties.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Submonoidproof · cited by 3,086
- IsLocalizationproof · cited by 636
- Submonoid.mapproof · cited by 190
- RingHom.IsStableUnderBaseChangestatement and proof · cited by 30
- RingHom.LocalizationPreservesstatement · cited by 13
- RingHom.IsStableUnderBaseChange.isLocalization_mapproof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- RingHom.Smooth.propertyIsLocalproof · cited by 5
- RingHom.finiteType_localizationPreservesproof · cited by 2
- RingHom.FormallyUnramified.propertyIsLocalproof · cited by 1
- RingHom.finitePresentation_localizationPreservesproof · cited by 1
- AlgebraicGeometry.LocallyOfFiniteType.stalkMapproof · cited by 1
- RingHom.FormallySmooth.localizationPreservesproof · cited by 0
- RingHom.QuasiFinite.propertyIsLocalproof · cited by 0
- RingHom.isStandardSmoothOfRelativeDimension_localizationPreservesproof · cited by 0
- AlgebraicGeometry.FormallyUnramified.stalkMapproof · cited by 0
- RingHom.isStandardSmooth_localizationPreservesproof · cited by 0
- RingHom.Flat.propertyIsLocalproof · cited by 0