Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.notMem_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)
  {x : IsDedekindDomain.HeightOneSpectrum.adicCompletion K v},
  x ∉ IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers K v ↔ 1 < Valued.v x

Defined in: Mathlib.RingTheory.DedekindDomain.AdicValuation
Cited by: 0 results in Mathlib
Foundations: Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDedekindDomain Field Algebra IsFractionRing

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WithZerostatement · cited by 586
IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
not_leproof · cited by 328
ValuationSubringstatement · cited by 187

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