Theorems · Definition · commutative algebra

IsFractionRing.ringEquivOfRingEquiv

{A : Type u_8} →
  {K : Type u_9} →
    {B : Type u_10} →
      {L : Type u_11} →
        [inst : CommRing A] →
          [inst_1 : CommRing B] →
            [inst_2 : CommRing K] →
              [inst_3 : CommRing L] →
                [inst_4 : Algebra A K] →
                  [IsFractionRing A K] → [inst_6 : Algebra B L] → [IsFractionRing B L] → A ≃+* B → K ≃+* L

Given rings A, B and localization maps to their fraction rings f : A →+* K, g : B →+* L, an isomorphism h : A ≃+* B induces an isomorphism of fraction rings K ≃+* L.

Defined in

Mathlib.RingTheory.Localization.FractionRing

Cited by

17 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingCommRingAlgebraIsFractionRingAlgebraIsFractionRing