English
For a field K, the prime ideal generated by X in PowerSeries K is the canonical height-one prime in the Dedekind spectrum of PowerSeries, i.e., the ideal (X) is prime and nonzero.
Русский
Для поля K единичная идеальная система генерируемая X в PowerSeries K является канонической простейшей высоты в спектре Демекентина: идеал (X) прост и не нулевой.
LaTeX
$$$\mathrm{idealX}\;K := \text{Ideal span }\{X\},\; \text{span}_{{}}(X) \text{ is prime and } X\neq 0.$$$
Lean4
/-- The prime ideal `(X)` of `K⟦X⟧`, when `K` is a field, as a term of the `HeightOneSpectrum`. -/
def idealX : IsDedekindDomain.HeightOneSpectrum K⟦X⟧
where
asIdeal := Ideal.span { X }
isPrime := PowerSeries.span_X_isPrime
ne_bot := by rw [ne_eq, Ideal.span_singleton_eq_bot]; exact X_ne_zero
