Theorems · Theorem · field theory
Field.exists_primitive_element_of_finite_intermediateField
∀ (F : Type u_1) (E : Type u_2) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [Finite (IntermediateField F E)] (K : IntermediateField F E), ∃ α, F⟮α⟯ = K
- Defined in
- Mathlib.FieldTheory.PrimitiveElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Top.topproof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Finitestatement and proof · cited by 3,029
- FiniteDimensionalproof · cited by 1,854
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinstatement and proof · cited by 382
- Infiniteproof · cited by 352
- finite_or_infiniteproof · cited by 50
- IntermediateField.liftproof · cited by 22
- IntermediateField.lift_topproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Field.exists_primitive_element_iff_finite_intermediateFieldproof · cited by 0