Theorems · Definition · commutative algebra

IsDedekindDomain.HeightOneSpectrum.adicCompletion.equiv

{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

adicCompletion.toCompletion as a ring isomorphism onto the underlying completion.

Defined in

Mathlib.RingTheory.DedekindDomain.AdicValuation

Cited by

2 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing