Theorems · Theorem · field theory
Field.nonempty_algHom_of_exists_root
∀ {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)- Defined in
- Mathlib.FieldTheory.Isaacs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites70
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by3
Results whose statement or proof uses this declaration.
- Field.nonempty_algHom_of_minpoly_eqproof · cited by 2
- IsAlgClosure.of_exists_rootproof · cited by 1
- Field.nonempty_algHom_of_exist_rootsproof · cited by 0