exists_primitive_element_of_finite_bot

English

Let F be a field and E a finite-dimensional extension of F which is finite over F; then there exists α ∈ E with F⟮α⟯ = ⊤.

Русский

Пусть F — поле, а E над F конечно удлинено; тогда существует α ∈ E such that F⟮α⟯ = ⊤.

LaTeX

$$$\exists \alpha\in E,\ F\langle \alpha\rangle = \top$$$

Lean4

/-- Primitive element theorem for finite-dimensional extension of a finite field. -/
theorem exists_primitive_element_of_finite_bot [Finite F] [FiniteDimensional F E] : ∃ α : E, F⟮α⟯ = ⊤ :=
  haveI : Finite E := Module.finite_of_finite F
  exists_primitive_element_of_finite_top F E

Похожие утверждения