Theorems · Definition · commutative algebra
LaurentSeries.powerSeriesRingEquiv
(K : Type u_2) →
[inst : Field K] →
PowerSeries K ≃+* ↥(IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers (RatFunc K) (Polynomial.idealX K))The ring isomorphism between K⟦X⟧ and the unit ball inside the X-adic completion of
K⟮X⟯.
- Defined in
- Mathlib.RingTheory.LaurentSeries
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- RingEquivstatement · cited by 1,147
- PowerSeriesstatement · cited by 797
- RatFuncstatement · cited by 301
- ValuationSubringstatement · cited by 187
- IsDedekindDomain.HeightOneSpectrum.adicCompletionstatement · cited by 93
- RingEquiv.transproof · cited by 54
- Polynomial.idealXstatement · cited by 23
- IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegersstatement · cited by 22
- LaurentSeries.LaurentSeriesRingEquivproof · cited by 8
- RingEquiv.subringCongrproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- LaurentSeries.powerSeriesRingEquiv_coe_applystatement · cited by 0