Theorems · Theorem · field theory
IntermediateField.exists_algHom_of_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 : E), IsIntegral F s ∧ (Polynomial.map (algebraMap F K) (minpoly F s)).Splits) →
∀ {x : E} {y : K}, (Polynomial.aeval y) (minpoly F x) = 0 → ∃ φ, φ x = y- Defined in
- Mathlib.FieldTheory.Extension
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- Set.univproof · cited by 3,945
- AlgHomstatement · cited by 3,236
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.aevalstatement and proof · cited by 615
- minpolystatement and proof · cited by 439
- IsIntegralstatement and proof · cited by 427
- Polynomial.Splitsstatement and proof · cited by 290
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.IsAlgebraic.normalClosure_eq_iSup_adjoin_of_splitsproof · cited by 3
- Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly_of_splitsproof · cited by 2
- IsConjRoot.exists_algEquivproof · cited by 1
- Normal.minpoly_eq_iff_mem_orbitproof · cited by 1