powerSeriesRingEquiv — Mathlib

English

The LaurentSeries Ring Equiv sends any f to an element lying in the valuation subring of the completion.

Русский

Лорентсово кольцо эквив sends любой элемент в ценностный подкольцо завершения.

LaTeX

$$$\\mathrm{LaurentSeriesRingEquiv}\\;K\\;f \\in \\mathrm{Valued.v}.\\mathrm{valuationSubring}$$$

Lean4

/-- The ring isomorphism between `K⟦X⟧` and the unit ball inside the `X`-adic completion of
`RatFunc K`. -/
abbrev powerSeriesRingEquiv : K⟦X⟧ ≃+* (idealX K).adicCompletionIntegers (RatFunc K) :=
  ((powerSeriesEquivSubring K).trans (LaurentSeriesRingEquiv K).subringMap).trans <|
    RingEquiv.subringCongr (powerSeries_ext_subring K)

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