Theorems · Theorem · commutative algebra

TensorProduct.sum_tmul

∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_7} {N : Type u_8} [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] {α : Type u_22} (s : Finset α) (m : α → M)
  (n : N), (∑ a ∈ s, m a) ⊗ₜ[R] n = ∑ a ∈ s, m a ⊗ₜ[R] n

Defined in

Mathlib.LinearAlgebra.TensorProduct.Defs

Cited by

6 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModule