Theorems · Theorem · field theory
IntermediateField.exists_algHom_of_adjoin_splits_of_aeval
∀ {F : Type u_1} {E : Type u_2} {K : Type u_3} [inst : Field F] [inst_1 : Field E] [inst_2 : Field K]
[inst_3 : Algebra F E] [inst_4 : Algebra F K] {S : Set E},
(∀ s ∈ S, IsIntegral F s ∧ (Polynomial.map (algebraMap F K) (minpoly F s)).Splits) →
∀ {x : E} {y : K}, IntermediateField.adjoin F S = ⊤ → (Polynomial.aeval y) (minpoly F x) = 0 → ∃ φ, φ x = y- Defined in
- Mathlib.FieldTheory.Extension
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgHomstatement and proof · cited by 3,236
- IntermediateFieldstatement · cited by 988
- Polynomial.mapstatement and proof · cited by 806
- AlgEquiv.symmproof · cited by 615
- Polynomial.aevalstatement and proof · cited by 615
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.exists_algHom_of_splits_of_aevalproof · cited by 4