Theorems · Definition · commutative algebra

IsLocalization.algEquiv

{R : Type u_1} →
  [inst : CommSemiring R] →
    (M : Submonoid R) →
      (S : Type u_2) →
        [inst_1 : CommSemiring S] →
          [inst_2 : Algebra R S] →
            [IsLocalization M S] →
              (Q : Type u_4) → [inst_4 : CommSemiring Q] → [inst_5 : Algebra R Q] → [IsLocalization M Q] → S ≃ₐ[R] Q

If S, Q are localizations of R at the submonoid M respectively, there is an isomorphism of localizations S ≃ₐ[R] Q.

Defined in

Mathlib.RingTheory.Localization.Basic

Cited by

45 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraIsLocalizationCommSemiringAlgebraIsLocalization