Theorems · Theorem · commutative algebra

IsLocalization.tensorProduct_tensorProduct_right

∀ (R : Type u_7) (S : Type u_8) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S] {A : Type u_9}
  [inst_3 : CommSemiring A] [inst_4 : Algebra R A] (M : Submonoid A) (B : Type u_10) [inst_5 : CommSemiring B]
  [inst_6 : Algebra R B] [inst_7 : Algebra A B] [IsScalarTower R A B] [IsLocalization M B]
  [inst_10 : Algebra (TensorProduct R S A) (TensorProduct R S B)]
  [IsScalarTower S (TensorProduct R S A) (TensorProduct R S B)],
  (algebraMap (TensorProduct R S A) (TensorProduct R S B)).comp Algebra.TensorProduct.includeRight.toRingHom =
      Algebra.TensorProduct.includeRight.comp (algebraMap A B) →
    IsLocalization (Submonoid.map Algebra.TensorProduct.includeRight M) (TensorProduct R S B)

S ⊗[R] A[M⁻¹] is the localization of S ⊗[R] A at M.

Defined in

Mathlib.RingTheory.Localization.BaseChange

Cited by

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraCommSemiringAlgebraCommSemiringAlgebraAlgebraIsScalarTowerIsLocalizationAlgebraIsScalarTower