Theorems · Theorem · commutative algebra
LaurentSeries.mem_integers_of_powerSeries
∀ (K : Type u_2) [inst : Field K] (F : PowerSeries K),
(LaurentSeries.LaurentSeriesRingEquiv K) ((HahnSeries.ofPowerSeries ℤ K) F) ∈
IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers (RatFunc K) (Polynomial.idealX K)Through the isomorphism LaurentSeriesRingEquiv, power series land in the unit ball inside the
completion of K⟮X⟯.
- Defined in
- Mathlib.RingTheory.LaurentSeries
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 184 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- RingEquivstatement · cited by 1,147
- Multiplicativeproof · cited by 875
- PowerSeriesstatement and proof · cited by 797
- WithZeroproof · cited by 586
- HahnSeriesstatement · cited by 528
- RatFuncstatement and proof · cited by 301
- ValuationSubringstatement · cited by 187
- IsDedekindDomain.HeightOneSpectrum.adicCompletionstatement · cited by 93
Cited by1
Results whose statement or proof uses this declaration.
- LaurentSeries.powerSeries_ext_subringproof · cited by 0