Theorems · Definition · commutative algebra
RingHom.StableUnderCompositionWithLocalizationAwaySource
({R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop) → PropA property P of ring homs satisfies RingHom.StableUnderCompositionWithLocalizationAwaySource
if whenever P holds for f it also holds for the composition with
localization maps on the source.
- Defined in
- Mathlib.RingTheory.LocalProperties.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 26 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.
- 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
- RingHom.compproof · cited by 899
- IsLocalization.Awayproof · cited by 218
Cited by7
Results whose statement or proof uses this declaration.
- RingHom.OfLocalizationSpanTarget.ofLocalizationSpanstatement and proof · cited by 7
- RingHom.StableUnderCompositionWithLocalizationAwayproof · cited by 6
- AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locallystatement and proof · cited by 3
- RingHom.locally_stableUnderCompositionWithLocalizationAwaySourcestatement and proof · cited by 3
- AlgebraicGeometry.HasRingHomProperty.respects_isOpenImmersionstatement and proof · cited by 1
- AlgebraicGeometry.HasRingHomProperty.iff_exists_appLEstatement and proof · cited by 0
- RingHom.locally_StableUnderCompositionWithLocalizationAwaySourcestatement · cited by 0