Theorems · Definition · commutative algebra

IsDedekindDomain.HeightOneSpectrum.adicCompletion.toCompletion

{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} →
                IsDedekindDomain.HeightOneSpectrum.adicCompletion K v →
                  (IsDedekindDomain.HeightOneSpectrum.valuation K v).Completion

The underlying element of the completion (v.valuation K).Completion.

Defined in

Mathlib.RingTheory.DedekindDomain.AdicValuation

Cited by

25 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing