Theorems · Theorem · commutative algebra

PiTensorProduct.smul_tprod_mul_smul_tprod

∀ {ι : Type u_1} {R : Type u_3} {A : ι → Type u_4} [inst : CommSemiring R]
  [inst_1 : (i : ι) → NonUnitalNonAssocSemiring (A i)] [inst_2 : (i : ι) → Module R (A i)]
  [inst_3 : ∀ (i : ι), SMulCommClass R (A i) (A i)] [inst_4 : ∀ (i : ι), IsScalarTower R (A i) (A i)] (r s : R)
  (x y : (i : ι) → A i),
  r • (PiTensorProduct.tprod R) x * s • (PiTensorProduct.tprod R) y = (r * s) • (PiTensorProduct.tprod R) (x * y)

Defined in

Mathlib.RingTheory.PiTensorProduct

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleSMulCommClassIsScalarTower