Theorems · Theorem · commutative algebra
RingHom.Flat.localRingHom
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S},
f.Flat →
∀ (P : Ideal S) [inst_2 : P.IsPrime] (Q : Ideal R) [inst_3 : Q.IsPrime] (hQP : Q = Ideal.comap f P),
(Localization.localRingHom Q P f hQP).Flat- Defined in
- Mathlib.RingTheory.RingHom.Flat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 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.
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerproof · cited by 3,896
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplstatement and proof · cited by 462
- Ideal.comapstatement and proof · cited by 443
- RingHom.toAlgebraproof · cited by 337
- Localization.AtPrimestatement and proof · cited by 299
- RingHom.Flatstatement and proof · cited by 60
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Flat.stalkMapproof · cited by 1