Theorems · Theorem · linear algebra

Submodule.tensorEquivSpan_apply_tmul

∀ {R : Type u_1} (A : Type u_2) {M : Type u_3} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A]
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module A M] [inst_6 : IsScalarTower R A M]
  (p : Submodule R M) [inst_7 : Algebra.IsEpi R A] [inst_8 : Module.Flat R A] (a : A) (x : ↥p),
  ↑((Submodule.tensorEquivSpan A p) (a ⊗ₜ[R] x)) = a • ↑x

Defined in

Mathlib.LinearAlgebra.Span.TensorProduct

Cited by

0 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAlgebra.IsEpiModule.Flat