Theorems · Definition · commutative algebra

Algebra.Presentation.tensorModelOfHasCoeffsEquiv

{R : Type u_1} →
  {S : Type u_2} →
    {ι : Type u_3} →
      {σ : Type u_4} →
        [inst : CommRing R] →
          [inst_1 : CommRing S] →
            [inst_2 : Algebra R S] →
              {P : Algebra.Presentation R S ι σ} →
                (R₀ : Type u_5) →
                  [inst_3 : CommRing R₀] →
                    [inst_4 : Algebra R₀ R] →
                      [inst_5 : Algebra R₀ S] →
                        [inst_6 : IsScalarTower R₀ R S] →
                          [inst_7 : P.HasCoeffs R₀] →
                            TensorProduct R₀ R (Algebra.Presentation.ModelOfHasCoeffs R₀) ≃ₐ[R] S

The natural isomorphism R ⊗[R₀] S₀ ≃ₐ[R] S.

Defined in

Mathlib.RingTheory.Extension.Presentation.Core

Cited by

4 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTowerAlgebra.Presentation.HasCoeffs