Theorems · Theorem · field theory
Field.exists_primitive_element_of_finite_bot
∀ (F : Type u_1) [inst : Field F] (E : Type u_2) [inst_1 : Field E] [inst_2 : Algebra F E] [Finite F] [FiniteDimensional F E], ∃ α, F⟮α⟯ = ⊤
Primitive element theorem for finite-dimensional extension of a finite field.
- Defined in
- Mathlib.FieldTheory.PrimitiveElement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.topstatement · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Finitestatement and proof · cited by 3,029
- FiniteDimensionalstatement and proof · cited by 1,854
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement · cited by 382
- Field.exists_primitive_element_of_finite_topproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Field.exists_primitive_elementproof · cited by 6
- Field.nonempty_algHom_of_exists_rootproof · cited by 3
- Field.exists_primitive_element_of_finite_intermediateFieldproof · cited by 1