Theorems · Theorem · field theory
Field.nonempty_algHom_of_minpoly_eq
∀ {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] [alg : Algebra.IsAlgebraic F E],
(∀ (x : E), ∃ y, minpoly F x = minpoly F y) → Nonempty (E →ₐ[F] K)- Defined in
- Mathlib.FieldTheory.Isaacs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.aevalproof · cited by 615
- minpolystatement and proof · cited by 439
- Algebra.IsAlgebraicstatement and proof · cited by 322
- minpoly.aevalproof · cited by 91
- Field.nonempty_algHom_of_exists_rootproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Field.nonempty_algHom_of_range_minpoly_subsetproof · cited by 1
- Field.nonempty_algHom_of_aeval_eq_zero_subsetproof · cited by 1