Theorems · Theorem · commutative algebra
TensorProduct.toIntegralClosure_mvPolynomial_bijective
∀ {R : Type u_1} {B : Type u_3} [inst : CommRing R] [inst_1 : CommRing B] [inst_2 : Algebra R B] {σ : Type u_4},
Function.Bijective ⇑(TensorProduct.toIntegralClosure R (MvPolynomial σ R) B)Base changing to MvPolynomial σ R preserves integral closure.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites77
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
- RingHomproof · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Finsuppstatement and proof · cited by 5,255
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- AlgHomstatement and proof · cited by 3,236
- TensorProductstatement and proof · cited by 2,545
- MvPolynomialstatement and proof · cited by 2,140
Cited by1
Results whose statement or proof uses this declaration.
- TensorProduct.toIntegralClosure_bijective_of_smoothproof · cited by 0