Theorems · Theorem · ring theory

TensorAlgebra.ofDirectSum_of_tprod

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {n : ℕ}
  (x : Fin n → M),
  TensorAlgebra.ofDirectSum ((DirectSum.of (fun n => TensorPower R n M) n) ((PiTensorProduct.tprod R) x)) =
    (TensorAlgebra.tprod R M n) x

Defined in

Mathlib.LinearAlgebra.TensorAlgebra.ToTensorPower

Cited by

2 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModule