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Theorems · Theorem · field theory

IsNormalClosure.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} [self : IsNormalClosure F K L] (x : K),
  (Polynomial.map (algebraMap F L) (minpoly F x)).Splits
Defined in
Mathlib.FieldTheory.Normal.Closure
Cited by
0 results in Mathlib
Foundations
Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
IsNormalClosure
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Around this declaration

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

IsNormalClosure.equiv · cited by 0IsNormalClosure.equivAlgebra · cited by 11388AlgebraField · cited by 7404FieldAlgebra.algebraMap · cited by 4706Algebra.algebraMapPolynomial.map · cited by 806Polynomial.mapminpoly · cited by 439minpolyPolynomial.Splits · cited by 290Polynomial.SplitsIsNormalClosure · cited by 5IsNormalClosureIsNormalClosure.splitsCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.