Theorems · Theorem · commutative algebra

Algebra.TensorProduct.basisAux_tmul

∀ {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) (m : M),
  (Algebra.TensorProduct.basisAux A b) (a ⊗ₜ[R] m) = a • Finsupp.mapRange ⇑(algebraMap R A) ⋯ (b.repr m)

Defined in

Mathlib.RingTheory.TensorProduct.Free

Cited by

2 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModule