algEquiv — Mathlib

English

There is an A-algebra isomorphism between FractionRing A and any K under IsFractionRing.

Русский

Существует A-алгебраическое изоморфизм FractionRing A и K под IsFractionRing.

LaTeX

$$FractionRing.algEquiv (A) (K) : FractionRing A ≃_A[A] K$$

Lean4

/-- Given a ring `A` and a localization map to a fraction ring
`f : A →+* K`, we get an `A`-isomorphism between the fraction ring of `A` as a quotient
type and `K`. -/
noncomputable def algEquiv (K : Type*) [CommRing K] [Algebra A K] [IsFractionRing A K] : FractionRing A ≃ₐ[A] K :=
  Localization.algEquiv (nonZeroDivisors A) K

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