Theorems · Definition · commutative algebra
Algebra.TensorProduct.quotIdealMapEquivQuotTensor
{A : Type u_1} →
(B : Type u_2) →
[inst : CommRing A] →
[inst_1 : CommRing B] →
[inst_2 : Algebra A B] → (I : Ideal A) → (B ⧸ Ideal.map (algebraMap A B) I) ≃ₐ[A ⧸ I] TensorProduct A (A ⧸ I) B(A ⧸ I) ⊗[A] B is isomorphic as an A ⧸ I-algebra to B ⧸ I B.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- TensorProductstatement and proof · cited by 2,545
- HasQuotient.Quotientstatement and proof · cited by 2,301
- AlgEquivstatement · cited by 1,681
- RingEquivproof · cited by 1,147
- Ideal.mapstatement and proof · cited by 692
- AlgEquiv.toRingEquivproof · cited by 137
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.TensorProduct.quotIdealMapEquivQuotTensor_mkstatement · cited by 0