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Theorems · Theorem · field theory

IsGalois.splits

∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] [IsGalois F E] (x : E),
  (Polynomial.map (algebraMap F E) (minpoly F x)).Splits
Defined in
Mathlib.FieldTheory.Galois.Basic
Cited by
2 results in Mathlib
Foundations
Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebraIsGalois
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Around this declaration

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

IsGalois.card_aut_eq_finrank · cited by 16IsGalois.card_aut_eq_finr…IsGalois.is_separable_splitting_field · cited by 2IsGalois.is_separable_spl…Algebra · cited by 11388AlgebraField · cited by 7404FieldAlgebra.algebraMap · cited by 4706Algebra.algebraMapPolynomial.map · cited by 806Polynomial.mapminpoly · cited by 439minpolyPolynomial.Splits · cited by 290Polynomial.SplitsIsGalois · cited by 149IsGaloisNormal.splits' · cited by 2Normal.splits'IsGalois.splitsCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.