Theorems · Theorem · commutative algebra

IsBaseChange.basis_repr_comp_apply

∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_2} [inst_1 : CommSemiring S] [inst_2 : Algebra R S] {V : Type u_3}
  [inst_3 : AddCommMonoid V] [inst_4 : Module R V] {W : Type u_4} [inst_5 : AddCommMonoid W] [inst_6 : Module R W]
  [inst_7 : Module S W] [inst_8 : IsScalarTower R S W] {ι : Type u_5} {ε : V →ₗ[R] W} (b : Module.Basis ι R V)
  (ibc : IsBaseChange S ε) (v : V) (i : ι), ((IsBaseChange.basis b ibc).repr (ε v)) i = (algebraMap R S) ((b.repr v) i)

Defined in

Mathlib.RingTheory.TensorProduct.IsBaseChangeFree

Cited by

3 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTower