transcendental_X — Mathlib

English

The underlying ideal of idealX K is the principal ideal generated by X: (idealX K).asIdeal = ⟨X⟩.

Русский

Поскольку идеал идеалаX является порождённым X, имеем: (idealX K).asIdeal = ⟨X⟩.

LaTeX

$$$ (\mathrm{Polynomial}.idealX K).\mathrm{asIdeal} = \mathrm{Ideal}.span\{ X \}$$$

Lean4

theorem transcendental_X : Transcendental K (X : RatFunc K) :=
  by
  rw [← RatFunc.algebraMap_X, transcendental_algebraMap_iff (algebraMap_injective K)]
  exact Polynomial.transcendental_X K

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