Theorems · Theorem · field theory

Field.nonempty_algHom_of_range_minpoly_subset

∀ {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],
  Set.range (minpoly F) ⊆ Set.range (minpoly F) → Nonempty (E →ₐ[F] K)

Defined in: Mathlib.FieldTheory.Isaacs
Cited by: 1 results in Mathlib
Foundations: Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Field Algebra Algebra Algebra.IsAlgebraic

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Polynomialstatement · cited by 5,681
Set.rangestatement and proof · cited by 4,705
AlgHomstatement · cited by 3,236
minpolystatement and proof · cited by 439
Algebra.IsAlgebraicstatement and proof · cited by 322
Field.nonempty_algHom_of_minpoly_eqproof · cited by 2

Cited by1

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Field.nonempty_algEquiv_of_range_minpoly_eqproof · cited by 0