Theorems · Theorem · commutative algebra
Module.Flat.of_flat_tensorProduct
∀ (R : Type u) (M : Type v) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (S : Type u_1) [inst_3 : CommRing S] [inst_4 : Algebra R S] [Module.FaithfullyFlat R S] [Module.Flat S (TensorProduct R S M)], Module.Flat R M
Flat descends along faithfully flat ring maps.
- 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.
Cites25
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
- TensorProductstatement and proof · cited by 2,545
- LinearMap.compproof · cited by 1,642
- LinearEquiv.symmproof · cited by 1,461
- TensorProduct.tmulproof · cited by 1,182
- LinearEquiv.toLinearMapproof · cited by 1,171
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.Smooth.of_smooth_tensorProduct_of_faithfullyFlatproof · cited by 2
- Module.Flat.iff_flat_tensorProductproof · cited by 0