Theorems · Definition · commutative algebra
RingHom.LocalizationAwayPreserves
({R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop) → PropA property P of ring homs is said to be preserved by localization away
if P holds for Rᵣ →+* Sᵣ whenever P holds for R →+* S.
- Defined in
- Mathlib.RingTheory.LocalProperties.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- IsLocalization.Awayproof · cited by 218
- IsLocalization.Away.mapproof · cited by 19
Cited by14
Results whose statement or proof uses this declaration.
- RingHom.LocalizationPreserves.awaystatement · cited by 9
- RingHom.LocalizationAwayPreserves.respectsIsostatement and proof · cited by 4
- RingHom.PropertyIsLocal.localizationAwayPreservesstatement · cited by 4
- AlgebraicGeometry.affineAnd_isLocalstatement and proof · cited by 2
- RingHom.LocalizationAwayPreserves.andstatement and proof · cited by 1
- AlgebraicGeometry.exists_basicOpen_le_appLE_of_appLE_of_isAffinestatement and proof · cited by 1
- RingHom.locally_localizationAwayPreservesstatement and proof · cited by 1
- RingHom.locally_propertyIsLocalstatement and proof · cited by 1
- AlgebraicGeometry.sourceAffineLocally_isLocalstatement and proof · cited by 1
- AlgebraicGeometry.HasRingHomProperty.locally_of_iffstatement and proof · cited by 0
- AlgebraicGeometry.HasAffineProperty.affineAnd_iffstatement and proof · cited by 0
- RingHom.PropertyIsLocal.casesOnstatement and proof · cited by 0