Theorems · Theorem · commutative algebra
Module.FaithfullyFlat.of_flat_of_isLocalHom
∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] [IsLocalRing A]
[IsLocalRing B] [Module.Flat A B] [IsLocalHom (algebraMap A B)], Module.FaithfullyFlat A BIf A is local and B is a local and flat A-algebra, then B is faithfully flat.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Submoduleproof · cited by 7,192
- Set.imageproof · cited by 5,609
- Idealproof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Ideal.mapproof · cited by 692
- Ideal.IsMaximalproof · cited by 452
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Flat.epi_of_flat_of_surjectiveproof · cited by 1
- CovBy.length_baseChangeproof · cited by 1
- IsLocalRing.length_baseChangeproof · cited by 1