isAlgebraic — Mathlib

English

If f ∈ K[X] and K ⊃ F with IsScalarTower, then L is algebraic over F.

Русский

Если f ∈ K[X] и существует IsScalarTower, то L алгебраически над F.

LaTeX

$$$\text{Isalgebraic}_{F\to L}$$$

Lean4

theorem isAlgebraic [Algebra F K] [Algebra F L] [Algebra.IsAlgebraic F K] [IsScalarTower F K L] (f : K[X])
    [IsSplittingField K L f] : Algebra.IsAlgebraic F L :=
  by
  have : FiniteDimensional K L := IsSplittingField.finiteDimensional L f
  exact Algebra.IsAlgebraic.trans F K L

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