Theorems · Theorem · commutative algebra
RingHom.Flat.comp
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
{f : R →+* S} {g : S →+* T}, f.Flat → g.Flat → (g.comp f).FlatComposition of flat ring homomorphisms is flat.
- Defined in
- Mathlib.RingTheory.RingHom.Flat
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- RingHom.compstatement and proof · cited by 899
- RingHom.toAlgebraproof · cited by 337
- IsScalarTower.of_algebraMap_eq'proof · cited by 101
- RingHom.Flatstatement and proof · cited by 60
- Module.Flat.transproof · cited by 9
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.finrank_SpecMap_eq_finrankproof · cited by 6
- RingHom.Flat.comp_iff_of_bijective_rightproof · cited by 2
- RingHom.Flat.stableUnderCompositionproof · cited by 2
- RingHom.Flat.comp_iff_of_bijective_leftproof · cited by 1
- RingHom.finrank_comp_right_of_bijectiveproof · cited by 1
- RingHom.Flat.ulift_iffproof · cited by 1
- Algebra.WeaklyEtale.transproof · cited by 0
- RingHom.Flat.tensorProductMapproof · cited by 0