Theorems · Definition · commutative algebra
RingHom.IsStableUnderBaseChange
({R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop) → PropA morphism property P is IsStableUnderBaseChange if P(S →+* A) implies
P(B →+* A ⊗[S] B).
- Defined in
- Mathlib.RingTheory.RingHomProperties
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
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
- IsScalarTowerproof · cited by 3,896
- Algebra.IsPushoutproof · cited by 59
Cited by30
Results whose statement or proof uses this declaration.
- RingHom.IsStableUnderBaseChange.mkstatement · cited by 16
- RingHom.IsStableUnderBaseChange.localizationPreservesstatement and proof · cited by 11
- RingHom.FormallyUnramified.isStableUnderBaseChangestatement · cited by 3
- RingHom.FormallySmooth.isStableUnderBaseChangestatement · cited by 2
- RingHom.isStandardSmoothOfRelativeDimension_isStableUnderBaseChangestatement · cited by 2
- RingHom.Smooth.isStableUnderBaseChangestatement and proof · cited by 2
- RingHom.finitePresentation_isStableUnderBaseChangestatement · cited by 2
- RingHom.IsStableUnderBaseChange.andstatement and proof · cited by 2
- RingHom.IsStableUnderBaseChange.pullback_fst_appTopstatement and proof · cited by 2
- RingHom.Flat.isStableUnderBaseChangestatement · cited by 1
- AlgebraicGeometry.HasRingHomProperty.isStableUnderBaseChangestatement and proof · cited by 1
- RingHom.QuasiFinite.isStableUnderBaseChangestatement · cited by 1