Theorems · Theorem · commutative algebra
Algebra.IsEffective.of_isEffective_tensorProduct_of_faithfullyFlat
∀ (R : Type u_3) [inst : CommRing R] (S : Type u_4) (T : Type u_5) [inst_1 : CommRing T] [inst_2 : Algebra R T] [inst_3 : Ring S] [inst_4 : Algebra R S] [Module.FaithfullyFlat R T], Algebra.IsEffective T (TensorProduct R T S) → Algebra.IsEffective R S
IsEffective descends along faithfully flat algebras.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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
- Ringstatement and proof · cited by 7,463
- TensorProductstatement and proof · cited by 2,545
- LinearMap.compproof · cited by 1,642
- TensorProduct.tmulproof · cited by 1,182
- LinearEquiv.toLinearMapproof · cited by 1,171
- AddMonoidHom.compproof · cited by 339
- AddMonoidHomClass.toAddMonoidHomproof · cited by 232
- LinearMap.restrictScalarsproof · cited by 215
- LinearMap.lTensorproof · cited by 203
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.IsEffective.of_faithfullyFlatproof · cited by 1