Theorems · Theorem · field theory

Algebra.IsAlgebraic.normalClosure_eq_iSup_adjoin_of_splits

∀ {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) →
    IntermediateField.normalClosure F K L = ⨆ x, IntermediateField.adjoin F ((minpoly F x).rootSet L)

Defined in

Mathlib.FieldTheory.Normal.Closure

Cited by

3 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldFieldAlgebraAlgebraAlgebra.IsAlgebraic