Theorems · Theorem · commutative algebra

Algebra.TensorProduct.basis_repr_symm_apply

∀ {R : Type u_1} {A : Type u_2} {M : Type uM} {ι : Type uι} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Algebra R A] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] (b : Module.Basis ι R M) (a : A) (i : ι),
  ((Algebra.TensorProduct.basis A b).repr.symm fun₀ | i => a) = a ⊗ₜ[R] b.repr.symm fun₀ | i => 1

Defined in

Mathlib.RingTheory.TensorProduct.Free

Cited by

2 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModule