Theorems · Theorem · commutative algebra
Algebra.Smooth.of_smooth_tensorProduct_of_faithfullyFlat
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (T : Type u_3)
[inst_3 : CommRing T] [inst_4 : Algebra R T] [Module.FaithfullyFlat R T] [Algebra.Smooth T (TensorProduct R T S)],
Algebra.Smooth R S- Defined in
- Mathlib.RingTheory.Etale.Descent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearEquivproof · cited by 3,317
- TensorProductstatement and proof · cited by 2,545
- AlgEquivproof · cited by 1,681
- TensorProduct.tmulproof · cited by 1,182
- AlgEquiv.symmproof · cited by 615
- Module.Flatproof · cited by 279
- KaehlerDifferentialproof · cited by 204
- AddEquiv.toEquivproof · cited by 174
- Module.FaithfullyFlatstatement and proof · cited by 72
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.Etale.of_etale_tensorProduct_of_faithfullyFlatproof · cited by 1
- RingHom.Smooth.codescendsAlong_faithfullyFlatproof · cited by 0