Theorems · Theorem · commutative algebra
Module.FaithfullyFlat.trans
∀ (R : Type u_1) [inst : CommRing R] (S : Type u_2) [inst_1 : CommRing S] [inst_2 : Algebra R S] (M : Type u_3) [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : Module S M] [IsScalarTower R S M] [Module.FaithfullyFlat R S] [Module.FaithfullyFlat S M], Module.FaithfullyFlat R M
If S is a faithfully flat R-algebra, then any faithfully flat S-Module is faithfully flat
as an R-module.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- LinearMapproof · cited by 10,215
- IsScalarTowerstatement and proof · cited by 3,896
- TensorProductproof · cited by 2,545
- map_zeroproof · cited by 1,614
- one_smulproof · cited by 1,374
- TensorProduct.tmulproof · cited by 1,182
Cited by2
Results whose statement or proof uses this declaration.
- RingHom.FaithfullyFlat.stableUnderCompositionproof · cited by 1
- Algebra.IsFiniteSplit.exists_tensorProduct_of_etaleproof · cited by 0