Theorems · Theorem · field theory
Field.nonempty_algHom_of_exist_roots
Deprecated since 2026-01-31Use Field.nonempty_algHom_of_exists_root instead.
∀ {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, (Polynomial.aeval y) (minpoly F x) = 0) → Nonempty (E →ₐ[F] K)Alias of Field.nonempty_algHom_of_exists_root.
- Defined in
- Mathlib.FieldTheory.Isaacs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement · cited by 11,388
- Fieldstatement · cited by 7,404
- Polynomialstatement · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.aevalstatement · cited by 615
- minpolystatement · cited by 439
- Algebra.IsAlgebraicstatement · cited by 322
- Field.nonempty_algHom_of_exists_rootproof · cited by 3
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