coeAlgHom — Mathlib

English

There is a canonical algebra homomorphism from the direct sum of submodules to the ambient algebra R.

Русский

Существует каноническое алгебра-гомоморфизм from прямого суммирования в алгебру R.

LaTeX

$$$$ DirectSum.co eAlgHom(A) : (⨁ i, A_i) \to_{algebra S} R. $$$$

Lean4

/-- The canonical algebra isomorphism between `⨁ i, A i` and `R`. -/
def coeAlgHom [AddMonoid ι] [CommSemiring S] [Semiring R] [Algebra S R] (A : ι → Submodule S R)
    [SetLike.GradedMonoid A] : (⨁ i, A i) →ₐ[S] R :=
  DirectSum.toAlgebra S _ (fun i => (A i).subtype) rfl (fun _ _ => rfl)

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