Theorems · Definition · field theory

IsNormalClosure.lift

{F : Type u_1} →
  {K : Type u_2} →
    {L : Type u_3} →
      [inst : Field F] →
        [inst_1 : Field K] →
          [inst_2 : Field L] →
            [inst_3 : Algebra F K] →
              [inst_4 : Algebra F L] →
                [h : IsNormalClosure F K L] →
                  {L' : Type u_4} →
                    [inst_5 : Field L'] →
                      [inst_6 : Algebra F L'] →
                        (∀ (x : K), (Polynomial.map (algebraMap F L') (minpoly F x)).Splits) → L →ₐ[F] L'

A normal closure of K/F embeds into any L/F where the minimal polynomials of K/F splits.

Defined in

Mathlib.FieldTheory.Normal.Closure

Cited by

0 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldFieldAlgebraAlgebraIsNormalClosureFieldAlgebra