Theorems · Definition · field theory

IsAlgClosure.equiv

(R : Type u) →
  [inst : CommRing R] →
    [IsDomain R] →
      (L : Type v) →
        (M : Type w) →
          [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 R L] → [inst_8 : Module.IsTorsionFree R L] → [IsAlgClosure R L] → L ≃ₐ[R] M

A (random) isomorphism between two algebraic closures of R.

Defined in: Mathlib.FieldTheory.IsAlgClosed.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDomain Field Field Algebra Module.IsTorsionFree IsAlgClosure Algebra Module.IsTorsionFree IsAlgClosure

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
IsDomainstatement and proof · cited by 2,196
AlgEquivstatement · cited by 1,681
Module.IsTorsionFreestatement and proof · cited by 600
AlgEquiv.ofBijectiveproof · cited by 34
IsAlgClosurestatement and proof · cited by 16
IsAlgClosed.liftproof · cited by 5

Cited by2

Results whose statement or proof uses this declaration.

IsAlgClosure.equivOfAlgebraic'proof · cited by 1
Algebra.isGeometricallyReduced_field_iffproof · cited by 1