Theorems · Theorem · linear algebra

TensorProduct.finsuppScalarRight_apply_tmul_apply

∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] {M : Type u_3}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module S M] [inst_6 : IsScalarTower R S M] {ι : Type u_5}
  [inst_7 : DecidableEq ι] (m : M) (p : ι →₀ R) (i : ι),
  ((TensorProduct.finsuppScalarRight R S M ι) (m ⊗ₜ[R] p)) i = p i • m

Defined in

Mathlib.LinearAlgebra.DirectSum.Finsupp

Cited by

3 results in Mathlib

Foundations

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

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerDecidableEq