Theorems · Definition · commutative algebra

minpoly.equivAdjoin

{R : Type u_1} →
  {S : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [IsDomain R] →
          [inst_3 : Algebra R S] →
            [IsIntegrallyClosed R] →
              [IsDomain S] →
                [Module.IsTorsionFree R S] → {x : S} → IsIntegral R x → AdjoinRoot (minpoly R x) ≃ₐ[R] ↥R[x]

The algebra isomorphism AdjoinRoot (minpoly R x) ≃ₐ[R] adjoin R x

Defined in

Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed

Cited by

4 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsDomainAlgebraIsIntegrallyClosedIsDomainModule.IsTorsionFree