Theorems · Definition · commutative algebra

IsLocalization.algebraTensorEquiv

{R : Type u_1} →
  [inst : CommSemiring R] →
    (S : Submonoid R) →
      (A : Type u_2) →
        [inst_1 : CommSemiring A] →
          [inst_2 : Algebra R A] →
            [IsLocalization S A] →
              (B : Type u_5) →
                (C : Type u_6) →
                  [inst_4 : Semiring B] →
                    [inst_5 : Algebra R B] →
                      [inst_6 : Algebra A B] →
                        [inst_7 : IsScalarTower R A B] →
                          [inst_8 : Semiring C] →
                            [inst_9 : Algebra R C] →
                              [inst_10 : Algebra A C] →
                                [IsScalarTower R A C] → TensorProduct A B C ≃ₐ[A] TensorProduct R B C

If A is a localization of R, tensoring two A-algebras over A is the same as tensoring them over R.

Defined in

Mathlib.RingTheory.Localization.BaseChange

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraIsLocalizationSemiringAlgebraAlgebraIsScalarTowerSemiringAlgebraAlgebraIsScalarTower