Theorems · Definition · field theory

IsAlgClosure.equivOfEquiv

{R : Type u} →
  {S : Type u_3} →
    (L : Type v) →
      (M : Type w) →
        [inst : CommRing R] →
          [inst_1 : CommRing S] →
            [inst_2 : Field L] →
              [inst_3 : Field M] →
                [inst_4 : Algebra R M] →
                  [inst_5 : Module.IsTorsionFree R M] →
                    [IsAlgClosure R M] →
                      [inst_7 : Algebra S L] →
                        [inst_8 : Module.IsTorsionFree S L] →
                          [IsAlgClosure S L] → [IsDomain R] → [IsDomain S] → S ≃+* R → L ≃+* M

Algebraic closure of isomorphic fields are isomorphic

Defined in

Mathlib.FieldTheory.IsAlgClosed.Basic

Cited by

5 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingFieldFieldAlgebraModule.IsTorsionFreeIsAlgClosureAlgebraModule.IsTorsionFreeIsAlgClosureIsDomainIsDomain