Theorems · Theorem · commutative algebra

Algebra.TensorProduct.mul_apply

∀ {R : Type uR} {A : Type uA} {B : Type uB} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A]
  [inst_2 : Module R A] [inst_3 : SMulCommClass R A A] [inst_4 : IsScalarTower R A A]
  [inst_5 : NonUnitalNonAssocSemiring B] [inst_6 : Module R B] [inst_7 : SMulCommClass R B B]
  [inst_8 : IsScalarTower R B B] (a₁ a₂ : A) (b₁ b₂ : B),
  (Algebra.TensorProduct.mul (a₁ ⊗ₜ[R] b₁)) (a₂ ⊗ₜ[R] b₂) = (a₁ * a₂) ⊗ₜ[R] (b₁ * b₂)

Defined in

Mathlib.RingTheory.TensorProduct.Basic

Cited by

0 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleSMulCommClassIsScalarTowerNonUnitalNonAssocSemiringModuleSMulCommClassIsScalarTower