Theorems · Theorem · field theory
IntermediateField.exists_algHom_of_adjoin_splits
∀ {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) →
∀ {L : IntermediateField F E} (f : ↥L →ₐ[F] K), IntermediateField.adjoin F S = ⊤ → ∃ φ, φ.comp L.val = f- Defined in
- Mathlib.FieldTheory.Extension
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgHomstatement and proof · cited by 3,236
- IntermediateFieldstatement and proof · cited by 988
- Polynomial.mapstatement and proof · cited by 806
- AlgEquiv.symmproof · cited by 615
- AlgHom.compstatement and proof · cited by 501
- minpolystatement and proof · cited by 439
- IsIntegralstatement and proof · cited by 427
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.nonempty_algHom_of_adjoin_splitsproof · cited by 1
- IntermediateField.exists_algHom_of_splitsproof · cited by 0