Theorems · Theorem · commutative algebra

Module.Basis.algebraMapCoeffs_repr

∀ {R : Type u_1} (A : Type u_3) {ι : Type u_5} {M : Type u_6} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : AddCommMonoid M] [inst_3 : Algebra R A] [inst_4 : Module A M] [inst_5 : Module R M]
  [inst_6 : IsScalarTower R A M] (b : Module.Basis ι R M) (h : Function.Bijective ⇑(algebraMap R A)) (m : M),
  (Module.Basis.algebraMapCoeffs A b h).repr m = Finsupp.mapRange ⇑(algebraMap R A) ⋯ (b.repr m)

Defined in

Mathlib.RingTheory.AlgebraTower

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAddCommMonoidAlgebraModuleModuleIsScalarTower