Theorems · Definition · commutative algebra

IsFractionRing.liftAlgHom

{R : Type u_1} →
  [inst : CommRing R] →
    {A : Type u_4} →
      [inst_1 : CommRing A] →
        {K : Type u_5} →
          [inst_2 : Field K] →
            {L : Type u_7} →
              [inst_3 : Field L] →
                [inst_4 : Algebra A K] →
                  [IsFractionRing A K] →
                    [inst_6 : Algebra R A] →
                      [inst_7 : Algebra R K] →
                        [IsScalarTower R A K] →
                          [inst_9 : Algebra R L] → {g : A →ₐ[R] L} → Function.Injective ⇑g → K →ₐ[R] L

AlgHom version of IsFractionRing.lift.

Defined in

Mathlib.RingTheory.Localization.FractionRing

Cited by

9 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingFieldFieldAlgebraIsFractionRingAlgebraAlgebraIsScalarTowerAlgebra