Theorems · Theorem · commutative algebra
Algebra.IsEffective.of_faithfullyFlat
∀ (R : Type u_3) [inst : CommRing R] (S : Type u_4) [inst_1 : CommRing S] [inst_2 : Algebra R S] [Module.FaithfullyFlat R S], Algebra.IsEffective R S
IsEffective R S is true for any faithfully flat R-algebra S.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Module.FaithfullyFlatstatement and proof · cited by 72
- Algebra.IsEffectivestatement · cited by 5
- Algebra.TensorProduct.lmul''proof · cited by 3
- Algebra.IsEffective.of_isEffective_tensorProduct_of_faithfullyFlatproof · cited by 1
- Algebra.IsEffective.of_sectionproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.codRestrictEqLocusPushoutCocone.bijective_of_faithfullyFlatproof · cited by 0