Theorems · Theorem · commutative algebra

TensorProduct.tmul_smul

∀ {R : Type u_1} {R' : Type u_4} [inst : CommSemiring R] [inst_1 : Monoid R'] {M : Type u_7} {N : Type u_8}
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N] [inst_4 : DistribMulAction R' M] [inst_5 : Module R M]
  [inst_6 : Module R N] [inst_7 : SMulCommClass R R' M] [inst_8 : DistribMulAction R' N]
  [TensorProduct.CompatibleSMul R R' M N] (r : R') (x : M) (y : N), x ⊗ₜ[R] (r • y) = r • x ⊗ₜ[R] y

Defined in

Mathlib.LinearAlgebra.TensorProduct.Defs

Cited by

33 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidAddCommMonoidDistribMulActionModuleModuleSMulCommClassDistribMulActionTensorProduct.CompatibleSMul