Theorems · Definition · commutative algebra

IsDedekindDomain.HeightOneSpectrum.adicCompletion.valueGroupEquiv

{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) →
                ↥(MonoidWithZeroHom.ofClass
                        (IsDedekindDomain.HeightOneSpectrum.adicCompletion.valuation K v)).valueGroup ≃*
                  ↥(MonoidWithZeroHom.ofClass Valued.v).valueGroup

The multiplicative equivalence between the value group of the completion's valuation, pulled back along equiv, and that of the completion.

Defined in

Mathlib.RingTheory.DedekindDomain.AdicValuation

Cited by

3 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing