Theorems · Definition · commutative algebra

IsDedekindDomain.HeightOneSpectrum.adicCompletion.valueGroupOrderIso

{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)).ValueGroup₀ ≃*o
                  (MonoidWithZeroHom.ofClass Valued.v).ValueGroup₀

The order-preserving multiplicative equivalence between the ValueGroup₀ 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 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing