Theorems · Theorem · commutative algebra
TensorProduct.toIntegralClosure_bijective_of_tower
∀ {R : Type u_1} {S : Type u_2} {B : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[inst_3 : CommRing B] [inst_4 : Algebra R B] {T : Type u_4} [inst_5 : CommRing T] [inst_6 : Algebra R T]
[inst_7 : Algebra S T] [IsScalarTower R S T],
Function.Bijective ⇑(TensorProduct.toIntegralClosure R S B) →
Function.Bijective ⇑(TensorProduct.toIntegralClosure S T (TensorProduct R S B)) →
Function.Bijective ⇑(TensorProduct.toIntegralClosure R T B)"Base change preserves integral closure" is stable under composition.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement and proof · cited by 3,236
- TensorProductstatement and proof · cited by 2,545
- AlgEquivproof · cited by 1,681
- one_smulproof · cited by 1,374
- Subalgebrastatement · cited by 1,353
- TensorProduct.tmulproof · cited by 1,182
- Function.Bijectivestatement and proof · cited by 863
- AlgEquiv.symmproof · cited by 615
Cited by1
Results whose statement or proof uses this declaration.
- TensorProduct.toIntegralClosure_bijective_of_smoothproof · cited by 0