Theorems · Definition · field theory

IsAlgClosure.equivOfAlgebraic

(K : Type u_1) →
  (J : Type u_2) →
    (L : Type v) →
      (M : Type w) →
        [inst : Field K] →
          [inst_1 : Field J] →
            [inst_2 : Field L] →
              [inst_3 : Field M] →
                [inst_4 : Algebra K M] →
                  [IsAlgClosure K M] →
                    [inst_6 : Algebra K J] →
                      [inst_7 : Algebra J L] →
                        [IsAlgClosure J L] →
                          [inst_9 : Algebra K L] → [IsScalarTower K J L] → [Algebra.IsAlgebraic K J] → L ≃ₐ[K] M

A (random) isomorphism between an algebraic closure of K and an algebraic closure of an algebraic extension of K

Defined in

Mathlib.FieldTheory.IsAlgClosed.Basic

Cited by

0 results in Mathlib

Foundations

Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldFieldFieldAlgebraIsAlgClosureAlgebraAlgebraIsAlgClosureAlgebraIsScalarTowerAlgebra.IsAlgebraic