Theorems · Theorem · commutative algebra
Algebra.FormallySmooth.flat_of_algHom_of_isNoetherianRing
∀ {R : Type u_1} {A : Type u_2} {S : Type u_3} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[inst_3 : CommRing S] [inst_4 : Algebra R S] (f : S →ₐ[R] A),
Function.Surjective ⇑f → ∀ [Module.Flat R S] [IsNoetherianRing S] [Algebra.FormallySmooth R A], Module.Flat R A- Defined in
- Mathlib.RingTheory.Smooth.Flat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- AlgHomstatement and proof · cited by 3,236
- LinearMap.extproof · cited by 844
- AlgHom.compproof · cited by 501
- RingHom.kerproof · cited by 363
- Module.Flatstatement and proof · cited by 279
- IsNoetherianRingstatement and proof · cited by 268
- AlgHom.toLinearMapproof · cited by 254
- AlgHom.idproof · cited by 196
- AdicCompletionproof · cited by 160
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.Smooth.flat_of_isNoetherianRingproof · cited by 0