topEquiv — Mathlib

English

The top subalgebra of a ring A with R-structure is isomorphic to A as an R-algebra.

Русский

Верхняя подалгебра кольца A с структурой R изоморфна A как R-алгебра.

LaTeX

$$$ \\text{topEquiv} : (\\top : \\mathrm{Subalgebra} R A) \\simeq_{R} A $$$

Lean4

/-- The top subalgebra is isomorphic to the algebra.

This is the algebra version of `Submodule.topEquiv`. -/
@[simps!]
def topEquiv : (⊤ : Subalgebra R A) ≃ₐ[R] A :=
  AlgEquiv.ofAlgHom (Subalgebra.val ⊤) toTop rfl rfl

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