Theorems · Theorem · field theory

Algebra.IsAlgebraic.isNormalClosure_normalClosure

∀ {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] [Algebra.IsAlgebraic F K],
  (∀ (x : K), (Polynomial.map (algebraMap F L) (minpoly F x)).Splits) →
    IsNormalClosure F K ↥(IntermediateField.normalClosure F K L)

normalClosure F K L is a valid normal closure if K/F is algebraic and all minimal polynomials of K/F splits in L/F.

Defined in

Mathlib.FieldTheory.Normal.Closure

Cited by

0 results in Mathlib

Foundations

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

Assumes

FieldFieldFieldAlgebraAlgebraAlgebra.IsAlgebraic