Theorems · Theorem · ring theory

Algebra.TensorProduct.cancelBaseChange_tmul

∀ (R : Type uR) (S : Type uS) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (T : Type u_3)
  (A : Type u_4) (B : Type u_5) [inst_3 : CommSemiring T] [inst_4 : CommSemiring A] [inst_5 : CommSemiring B]
  [inst_6 : Algebra R T] [inst_7 : Algebra R A] [inst_8 : Algebra R B] [inst_9 : Algebra T A]
  [inst_10 : IsScalarTower R T A] [inst_11 : Algebra S A] [inst_12 : IsScalarTower R S A] [inst_13 : Algebra S T]
  [inst_14 : IsScalarTower S T A] (a : A) (s : S) (b : B),
  (Algebra.TensorProduct.cancelBaseChange R S T A B) (a ⊗ₜ[S] (s ⊗ₜ[R] b)) = (s • a) ⊗ₜ[R] b

Defined in

Mathlib.RingTheory.TensorProduct.Maps

Cited by

5 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraCommSemiringCommSemiringCommSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerAlgebraIsScalarTower