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Theorems · Theorem · field theory

IsNormalClosure.adjoin_rootSet

∀ {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, IntermediateField.adjoin F ((minpoly F x).rootSet L) = ⊤
Defined in
Mathlib.FieldTheory.Normal.Closure
Cited by
0 results in Mathlib
Foundations
Depth 132 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.lift · cited by 0IsNormalClosure.liftAlgebra · cited by 11388AlgebraTop.top · cited by 9680Top.topField · cited by 7404FieldiSup · cited by 2415iSupIntermediateField · cited by 988IntermediateFieldminpoly · cited by 439minpolyIntermediateField.adjoin · cited by 382IntermediateField.adjoinPolynomial.rootSet · cited by 101Polynomial.rootSetIsNormalClosure · cited by 5IsNormalClosureIsNormalClosure.adjoin_rootSetCITED BYCITES

Cites9

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Cited by1

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