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Theorems · Theorem · field theory

AlgHom.normal_bijective

∀ (F : Type u_1) (K : Type u_2) [inst : Field F] [inst_1 : Field K] [inst_2 : Algebra F K] (E : Type u_3)
  [inst_3 : Field E] [inst_4 : Algebra F E] [inst_5 : Algebra K E] [IsScalarTower F K E] [h : Normal F E]
  (ϕ : E →ₐ[F] K), Function.Bijective ⇑ϕ
Defined in
Mathlib.FieldTheory.Normal.Defs
Cited by
2 results in Mathlib
Foundations
Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebraFieldAlgebraAlgebraIsScalarTowerNormal
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Around this declaration

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

IsConjRoot.exists_algEquiv · cited by 1IsConjRoot.exists_algEquivNormal.minpoly_eq_iff_mem_orbit · cited by 1Normal.minpoly_eq_iff_mem…DFunLike.coe · cited by 62936DFunLike.coeAlgebra · cited by 11388AlgebraField · cited by 7404FieldIsScalarTower · cited by 3896IsScalarTowerAlgHom · cited by 3236AlgHomFunction.Bijective · cited by 863Function.BijectiveNormal · cited by 92NormalAlgebra.IsAlgebraic.bijective_of_isScalarTower' · cited by 1IsAlgebraic.bijective_of_…AlgHom.normal_bijectiveCITED 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.