Theorems · Definition · commutative algebra
IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers
{R : Type u_1} →
[inst : CommRing R] →
[inst_1 : IsDedekindDomain R] →
(K : Type u_2) →
[inst_2 : Field K] →
[inst_3 : Algebra R K] →
[inst_4 : IsFractionRing R K] →
(v : IsDedekindDomain.HeightOneSpectrum R) →
ValuationSubring (IsDedekindDomain.HeightOneSpectrum.adicCompletion K v)The ring of integers of adicCompletion.
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- ValuationSubringstatement · cited by 187
- Valued.vproof · cited by 163
- IsDedekindDomain.HeightOneSpectrum.adicCompletionstatement · cited by 93
- Valuation.valuationSubringproof · cited by 56
Cited by28
Results whose statement or proof uses this declaration.
- IsDedekindDomain.FiniteAdeleRingproof · cited by 9
- IsDedekindDomain.HeightOneSpectrum.mem_adicCompletionIntegersstatement · cited by 5
- Rat.HeightOneSpectrum.adicCompletionIntegers.padicIntEquivstatement and proof · cited by 4
- PadicInt.adicCompletionIntegersEquivstatement · cited by 2
- LaurentSeries.exists_powerSeries_of_memIntegersstatement and proof · cited by 1
- Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_applystatement and proof · cited by 1
- LaurentSeries.mem_integers_of_powerSeriesstatement · cited by 1
- LaurentSeries.powerSeriesRingEquivstatement · cited by 1
- IsDedekindDomain.FiniteAdeleRing.isUnit_iffproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.integersstatement and proof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.isUnit_iff_valued_eq_onestatement and proof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_onestatement and proof · cited by 1