Theorems · Definition · commutative algebra

Algebra.TensorProduct.quotIdealMapEquivTensorQuot

{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[B] TensorProduct A B (A ⧸ I)

B ⊗[A] (A ⧸ I) is isomorphic as a B-algebra to B ⧸ I B.

Defined in

Mathlib.RingTheory.TensorProduct.Quotient

Cited by

5 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra